Abstract:
Tunable fluid ends reduce valve-generated vibration to increase fluid-end reliability. Tunable fluid end embodiments comprise a family, each family member comprising a fluid end housing with at least one installed tunable component chosen from: tunable check valve assemblies, tunable valve seats, tunable radial arrays and/or tunable plunger seals. Each tunable component, in turn, contributes to blocking excitation of fluid end resonances, thus reducing the likelihood of fluid end failures associated with fatigue cracking and/or corrosion fatigue. By down-shifting the frequency domain of each valve-closing impulse shock, initial excitation of fluid end resonances is minimized. Subsequent damping and/or selective attenuation of vibration likely to excite one or more predetermined (and frequently localized) fluid end resonances represents further optimal use of fluid end vibration-control resources.

Description:
FIELD OF THE INVENTION 
     The invention relates generally to reciprocating pumps, and more specifically to vibration and vibration effects in such pumps. 
     BACKGROUND 
     Reciprocating high-pressure pumps (commonly called fracking or frac pumps) are often used in oil and gas fields for hydraulic fracturing of rock formations to increase hydrocarbon yields. Such pumps are typically truck-mounted for easy relocation from well-to-well. And they are usually designed in two sections: the (proximal) power section (herein “power end”) and the (distal) fluid section (herein “fluid end”). Each pump fluid end comprises at least one subassembly (and commonly three or more in a single fluid end housing), with each subassembly comprising a suction valve, a discharge valve, a plunger or piston, and a portion of (or substantially the entirety of) a pump fluid end subassembly housing (shortened herein to “pump housing” or “fluid end housing” or “housing” depending on the pump configuration). 
     For each pump fluid end subassembly, its fluid end housing comprises a pumping chamber in fluid communication with a suction bore, a discharge bore, and a piston/plunger bore. A suction valve (i.e., a check valve) within the suction bore, together with a discharge valve (i.e., another check valve) within the discharge bore, control bulk fluid movement from suction bore to discharge bore via the pumping chamber. Pulsatile fluid flow through the pump results from periodic pressurization of the pumping chamber by a reciprocating plunger or piston within the plunger/piston bore. Suction and pressure strokes alternately produce wide pressure swings in the pumping chamber (and across the suction and discharge check valves) as the reciprocating plunger or piston is driven by the pump power end. 
     Such pumps are rated at peak pumped-fluid pressures in current practice up to about 22,000 psi, while simultaneously being weight-limited due to the carrying capacity of the trucks on which they are mounted. (See, e.g., U.S. Pat. No. 7,513,759 B1, incorporated by reference). 
     Due to high peak pumped-fluid pressures, suction check valves experience particularly wide pressure variations between a suction stroke, when the valve opens, and a pressure stroke, when the valve closes. For example, during a pressure stroke a conventionally rigid/heavy check valve body (with pressurized fluid behind it) may be driven longitudinally toward metal-to-metal impact on a conventional frusto-conical valve seat at closing forces of about 50,000 to over 150,000 pounds. Total check valve-closure impact energy (i.e., the kinetic energy present at valve seat impact) is thus converted to a short-duration high-amplitude valve-closure impulse (i.e., a mechanical shock). Repeated application of such a valve-closure shock with each pump cycle predisposes the check valve, and the fluid end housing in which it is installed, to vibration-induced damage. Cumulative shocks thus constitute a significant liability imposed on frac pump reliability, proportional in part to the rigidity and weight of the check valve body. 
     The emergence of new frac pump reliability issues has paralleled the inexorable rise of peak pumped-fluid pressures in new fracking applications. And insight into these new pump failure modes can be gained through review of earlier shock and vibration studies, data from which are cited herein. For example, a recent treatise on the subject describes a mechanical shock “ . . . in terms of its inherent properties, in the time domain or in the frequency domain; and . . . in terms of the effect on structures when the shock acts as the excitation.” (see p. 20.5 of  Harris&#39; Shock and Vibration Handbook, Sixth Edition , ed. Allan G. Piersol and Thomas L. Paez, McGraw Hill (2010), hereinafter  Harris ). The above time and frequency domains are mathematically represented on opposite sides of equations generally termed Fourier transforms. And estimates of a shock&#39;s structural effects are frequently described in terms of two parameters: (1) the structure&#39;s undamped natural frequency and (2) the fraction of critical structural damping or, equivalently, the resonant gain Q (see  Harris  pp. 7.6, 14.9-14.10, 20.10). (See also, e.g., U.S. Pat. No. 7,859,733 B2, incorporated by reference). 
     Mathematical representations of time and frequency domain data play important roles in computer-assisted analysis of mechanical shock. In addition, shock properties are also commonly represented graphically as time domain impulse plots (e.g., acceleration vs. time) and frequency domain vibration plots (e.g., spectrum amplitude vs. frequency). Such graphical presentations readily illustrate the shock effects of metal-to-metal valve-closure, wherein longitudinal movement of a check valve body is abruptly stopped by a valve seat. Relatively high acceleration values and broad vibration spectra are prominent, each valve-closure impulse response primarily representing a violent conversion of kinetic energy to other energy forms. 
     Since energy cannot be destroyed, and since a conventional valve can neither store nor convert (i.e., dissipate) more than a small fraction of the valve-closure impulse&#39;s kinetic energy, most of that energy is necessarily transmitted to the pump housing. In a time domain plot, the transmitted energy appears as a high-amplitude impulse of short duration. And a corresponding frequency domain plot of transmitted energy reveals a broad-spectrum band of high-amplitude vibration. This means that nearly all of the check valve&#39;s cyclical valve-closure kinetic energy is converted to vibration energy. The overall effect of check valve closure may thus be compared to striking the valve seat repeatedly with a commercially-available impulse hammer. Such hammers are easily configured to produce relatively broad-spectrum high-amplitude excitation (i.e., vibration) in an object struck by the hammer. (See, e.g.,  Introduction to Impulse Hammers  at http://www.dytran.com/img/tech/a11.pdf, and  Harris  p. 20.10). 
     Summarizing then, relatively broad-spectrum high-amplitude vibration predictably results from a typical high-energy valve-closure impulse. And frac pumps with conventionally-rigid valves can suffer hundreds of these impulses per minute. Nearly all of this vibration energy is quickly transmitted to proximate areas of the fluid end or pump housing where it can be expected to excite damaging resonances that predispose the housing to fatigue failures. (See, e.g., U.S. Pat. No. 5,979,242, incorporated by reference). If, as expected, a natural resonance frequency of the housing coincides with a frequency within the valve-closure vibration spectrum, fluid end vibration amplitude may be substantially increased and the corresponding vibration fatigue damage made much worse. (See  Harris , p. 1.3). 
     Opportunities to limit fluid end damage begin with experiment-based redesign to control vibration fatigue. For example, a spectrum of vibration frequencies initially applied as a test can reveal structural resonance frequencies likely to cause trouble. Specifically, the applied vibration of a half-sine shock pulse of duration one millisecond has predominant spectral content up to about 2 kHz (see  Harris , p. 11.22), likely overlapping a plurality of fluid end housing natural frequencies. Such tests particularly focus attention on blocking progression of fatigue crack growth to the critical size for catastrophic fracture. Note that stronger housings aren&#39;t necessarily better in such cases, since increasing the housing&#39;s yield strength causes a corresponding decrease in critical crack size. (See  Harris , p. 33.23). 
     It might be assumed that certain valve redesigns proposed in the past (including relatively lighter valve bodies) would have alleviated at least some of the above failure modes. (See, e.g., U.S. Pat. No. 7,222,837 B1, incorporated by reference). But such redesigns emerged (e.g., in 2005) when fluid end peak pressures were generally substantially lower than they currently are. In relatively lower pressure applications (e.g., mud pumps), rigid/heavy valve bodies performed well because the valve-closure shocks and associated valve-generated vibration were less severe compared to shock and vibration experienced more recently in higher pressure applications (e.g., fracking) Thus, despite their apparent functional resemblance to impulse hammers, relatively rigid/heavy valves have been pressed into service as candidates for use in frac pump fluid ends. Indeed, they have generally been the only valves available in commercial quantities during the recent explosive expansion of well-service fracking operations. Substantially increased fluid end failure rates (due, e.g., to cracks near a suction valve seat deck) have been among the unfortunate, and unintended, consequences. 
     Such baleful vibration-related results in fluid ends might usefully be compared with vibration-related problems seen during the transition from slow-turning two-cylinder automobile engines to higher-speed and higher-powered inline six-cylinder engines around the years 1903-1910. Important torsional-vibration failure modes suddenly became evident in new six-cylinder engines, though they were neither anticipated nor understood at the time. Whereas the earlier engines had been under-powered but relatively reliable, torsional crankshaft vibrations in the six-cylinder engines caused objectionable noise (“octaves of chatter from the quivering crankshaft”) and unexpected catastrophic failures (e.g., broken crankshafts). (Quotation cited on p. 13 of  Royce and the Vibration Damper , Rolls-Royce Heritage Trust, 2003). Torsional-vibration was identified as the culprit and, though never entirely eliminated, was finally reduced to a relatively minor maintenance issue after several crankshaft redesigns and the development of crankshaft vibration dampers pioneered by Royce and Lanchester. 
     Reducing the current fluid end failure rates related to valve-generated vibration in frac pumps requires an analogous modern program of intensive study and specific design changes. The problem will be persistent because repeatedly-applied valve-closure energy impulses cannot be entirely eliminated in check-valve-based fluid end technology. So the valve-closing impulses must be modified, and their associated vibrations damped, to reduce excitation of destructive resonances in valves, pump housings, and related fluid end structures. Alternate materials, applied via innovative designs, illuminate the path forward now as they have in the past. Broad application of such improvements promises higher frac pump reliability, an important near-term goal. Simultaneously, inhibition of corrosion fatigue throughout analogous fluid circuits would be advanced, a longer-term benefit in refineries, hydrocarbon crackers and other industrial venues that are also subjected to shock-related vibration. 
     SUMMARY OF THE INVENTION 
     Tunable fluid ends reduce valve-generated vibration to increase fluid-end reliability. Tunable fluid end embodiments comprise a family, each family member comprising a pump housing with at least one installed tunable component chosen from: tunable check valve assemblies, tunable valve seats, tunable radial arrays and/or tunable plunger seals. Each tunable component, in turn, contributes to blocking excitation of fluid end resonances, thus reducing the likelihood of fluid end failures associated with fatigue cracking and/or corrosion fatigue. By down-shifting the frequency domain of each valve-closing impulse shock, initial excitation of fluid end resonances is minimized. Subsequent damping and/or selective attenuation of vibration likely to excite one or more predetermined (and frequently localized) fluid end resonances represents optimal employment of vibration-control resources. 
     Frequency domain down-shifting and damping both assist vibration control by converting valve-closure energy to heat and dissipating it in each tunable component present in a tunable fluid end embodiment. Effects of down-shifting on a valve-closure impulse shock include frequency-selective spectrum-narrowing that is easily seen in the frequency domain plot of each shock. That is, down-shifting effectively attenuates and/or limits the bandwidth(s) of valve-generated vibration. Subsequent (coordinated) damping assists in converting a portion of this band-limited vibration to heat. 
     Both down-shifting and damping are dependent in part on constraints causing shear-stress alteration (that is, “tuning”) imposed on one or more viscoelastic and/or shear-thickening elements in each tunable component. Additionally, hysteresis or internal friction (see  Harris , p. 5.7) associated with mechanical compliance of certain structures (e.g., valve bodies or springs) may aid damping by converting vibration energy to heat (i.e., hysteresis loss). (See  Harris,  p. 2.18). 
     Tunable component resonant frequencies may be shifted (or tuned) to approximate predetermined values corresponding to measured or estimated pump or fluid end housing resonant frequencies (herein termed “critical” frequencies). Such coordinated tuning predisposes valve-generated vibration at critical frequencies to excite the tunable component (and thus be damped and dissipated as heat) rather than exciting the housing itself (and thus predispose it to vibration fatigue-related cracking). 
     To complement the above coordinated damping, frequency down-shifting functions to reduce the total amount of critical frequency vibration requiring damping. Such down-shifting is activated through designs enhancing mechanical compliance. In continuous pump operation, mechanical compliance is manifest, for example, in elastic valve body flexures secondary to repetitive longitudinal compressive forces (i.e., plunger pressure strokes). Each such flexure is followed by a hysteresis-limited elastic rebound, the duration of the entire flexure-rebound interval being termed herein “rebound cycle time.” The inverse of rebound cycle time is termed herein “rebound characteristic frequency.” Cumulative rebound cycle energy loss in the form of heat (e.g., hysteresis loss plus friction loss) is continuously transported for redistribution within the valve body and eventual rejection to the valve body surroundings (including, e.g., the pumped fluid). This heat loss represents a reduction in the available energy content (and thus the damage-causing potential) of the valve-closure energy impulse. 
     Note that lengthening rebound cycle time to beneficially narrow the valve-generated vibration spectrum is accomplished in various invention embodiments using mechanical/hydraulic/pneumatic analogs of electronic wave-shaping techniques. For example, lengthened rebound cycle time is substantially influenced by the tunable valve assembly&#39;s increased longitudinal compliance associated with rolling seal contact (i.e., comprising valve body flexure and rebound) described herein between the valve body&#39;s peripheral valve seat interface and the tunable valve seat&#39;s mating surface. 
     Briefly summarizing, as each tunable component present in a tunable fluid end embodiment absorbs, converts and redistributes (i.e., dissipates) a portion of valve closing impulse shock energy, only a fraction of the original closing impulse energy remains at critical frequencies capable of exciting destructive resonant frequencies in the fluid end. Following vibration down-shifting, a significant portion of valve-closure energy has been shifted to lower frequency vibration through structural compliance as described above. This attenuated vibration is then selectively damped (i.e., dissipated as heat) at shifted frequencies via one or more of the tunable components. While tunable components may be relatively sharply tuned (e.g., to act as tuned mass dampers for specific frequencies), they may alternately be more broadly tuned to account for a range of vibration frequencies encountered in certain pump operations. Flexibility in tuning procedures, as described herein with material and adjustment choices, is therefore desirable. 
     Note that vibration absorption at specific frequencies (e.g., via dynamic or tuned absorbers) may have limited utility in frac pumps because of the varying speeds at which the pumps operate and the relatively broad bandwidths associated with valve-closing impulse shocks. In contrast, the process of down-shifting followed by damping is more easily adapted to changes inherent in the pumps&#39; operational environment. Damping may nevertheless be added to a dynamic absorber to increase its effective frequency range for certain applications. (See, e.g., tuned vibration absorber and tuned mass damper in ch. 6 of  Harris ). 
     Selective damping of vibration frequencies near the resonant frequencies of fluid ends is desirable for the same reason that soldiers break step when they march over a bridge—because even relatively small amounts of vibration energy applied at the bridge&#39;s resonant frequency can cause catastrophic failure. Similar reasoning underlies the functions of selective vibration down-shifting and damping in tunable fluid ends. Various combinations of the tunable components described herein are particularly beneficial because they focus the functions of vibration-limiting resources on minimization of vibration energy present in a fluid end near its housing&#39;s critical frequencies. Cost and complexity of tunable components are thus minimized while the efficacy of each tunable component&#39;s function (i.e., vibration limitation at particular frequencies) is enhanced. Stated another way, a tunable component&#39;s selective vibration down-shifting and damping are optimized using metrics including cost, complexity, and damping factor (or degree of damping). 
     Note that a variety of optimization strategies for vibration attenuation and damping may be employed in specific cases, depending on parameters such as the Q (or quality) factor attributable to each fluid end resonance. The fluid end response to excitation of a resonance may be represented graphically as, for example, a plot of amplitude vs. frequency. Such a Q response plot typically exhibits a single amplitude maximum at the local fluid end resonance frequency, with decreasing amplitude values at frequencies above and below the resonance. At an amplitude value about 0.707 times the maximum value (i.e., the half-power point), the amplitude plot corresponds not to a single frequency but to a bandwidth between upper and lower frequency values on either side of the local fluid end resonance. The quality factor Q is then estimated as the ratio of the resonance frequency to the bandwidth. (See, e.g., pp. 2-18, 2-19 of  Harris ). (See also U.S. Pat. No. 7,113,876 B2, incorporated by reference). 
     Lower Q connotes the presence of more damping and a wider bandwidth (i.e., a relatively broader band of near-resonant frequencies). And higher Q connotes less damping and a narrower bandwidth (ideally, zero damping and a single resonant frequency). Since ideal fluid end resonances are not encountered in practice, optimization strategies typically include choice of the peak resonant frequency and Q of the tunable component in light of the peak resonant frequency and Q of the fluid end resonance of interest. Tunable component resonant frequencies identified herein as “similar” to fluid end or pump housing resonances are thus understood to lie generally in the frequency range indicated by the upper and lower frequency values of the relevant Q response half-power bandwidth. 
     In tunable components of the invention, choice of Q depends on both materials and structure, especially structural compliances and the properties of viscoelastic and/or shear-thickening materials present in the component(s). Further, the peak (or representative) frequency of a tunable component or a fluid end resonance may not be unambiguously obtainable. Thus, optimization of tunable component vibration damping may be an iterative empirical process and may not be characterized by a single-valued solution. Note also that tunable component resonant frequencies may be intentionally “detuned” (i.e., adjusted to slightly different values from nominal resonant or peak frequencies) in pursuit of an overall optimization strategy. 
     To minimize fluid end fatigue failures then, resonant frequencies of each tunable component of the invention are adjusted (i.e., tuned) using analytical and/or empirical frequency measures. Such measures are considered in light of the resonant frequencies of any other tunable component(s) present, and also in light of critical resonances of the fluid end or pump itself. The objective is optimal attenuation and damping of the most destructive portion(s) of valve-generated vibration. In each case, optimal vibration limitation will be dependent on the component&#39;s capacity to dissipate heat generated through hysteresis, friction and/or fluid turbulence. Thus, certain predetermined portion(s) of valve-closure energy are dissipated at one or more predetermined pump housing resonant (critical) frequencies. 
     Note that the critical frequencies proximate to a fluid end suction bore may differ, for example, from the critical frequencies proximate to the same fluid end&#39;s plunger bore due to the different constraints imposed by structures proximate the respective bores. Such differences are accounted for in the adjustment of tunable components, particularly tunable valve seats and tunable plunger seals. 
     What follows are descriptions of the structure and function of each tunable component that may be present in a tunable fluid end embodiment, the fluid end having at least one fluid end resonant frequency. Each tunable fluid end embodiment comprises at least one subassembly, and each subassembly comprises a housing (e.g., a fluid end housing or pump housing with appropriate bores). Within each housing&#39;s respective bores are a suction valve, a discharge valve, and a plunger or piston. When a tunable fluid end comprises multiple subassemblies (which is the general case), the respective subassembly housings are typically combined in a single fluid end housing. And at least one subassembly has at least one tunable component. In specific tunable fluid end embodiments, tunable components may be employed singly or in various combinations, depending on operative requirements. 
     The first tunable component described herein is a tunable check valve assembly (one being found in each tunable check valve). Installed in a fluid end for high pressure pumping, a tunable check valve assembly comprises at least one vibration damper or, in certain embodiments, a plurality of (radially-spaced) vibration dampers disposed in a valve body. Each vibration damper constitutes at least one tunable structural feature. Since the fluid end has at least a first fluid end resonance frequency, at least one vibration damper has (i.e., is tuned to) at least a first predetermined assembly resonant frequency similar to the first fluid end resonance (i.e., resonant frequency). If, for example, the fluid end has a second fluid end resonance frequency (a common occurrence), a single vibration damper and/or at least one of a plurality of vibration dampers may have (i.e., be tuned to) at least a second predetermined assembly resonant frequency similar to the second fluid end resonance frequency. In general, the specific manner of damping either one or a plurality of fluid end resonance frequencies with either one or a plurality (but not necessarily the same number) of vibration dampers is determined during the optimization process noted above. 
     Each of the sample embodiments of tunable check valve assemblies schematically illustrated herein comprises a check valve body having guide means (to maintain valve body alignment during longitudinal movement) and a peripheral valve seat interface. A peripheral groove spaced radially apart from a central reservoir is present in certain embodiments, and a viscoelastic element may be present in the peripheral groove (i.e., the groove damping element). In one such embodiment, the assembly&#39;s vibration dampers comprise a plurality of radially-spaced viscoelastic body elements disposed in the groove and reservoir, the viscoelastic groove element comprising a groove circumferential tubular area. The viscoelastic reservoir damping element may be tuned, for example, via a flange centrally coupled to the valve body. The reservoir damping element tuning frequency may be, as noted above, a first predetermined assembly resonant frequency similar to a first fluid end resonance. Analogously, the groove circumferential tubular area may comprise at least one shear thickening material providing the means to tune the groove damping element to at least a second predetermined assembly resonant frequency similar, for example, to either a first or second fluid end resonant frequency. The choice of tuning frequencies for the reservoir and groove damping elements is not fixed, but is based on a chosen optimization strategy for vibration damping in each fluid end. 
     Note that phase shifts inherent in the (nonlinear) operation of certain vibration dampers described herein create the potential for a plurality of resonant frequencies in a single vibration damper. 
     Note also that the longitudinal compliance of a tunable check valve assembly affects its rebound cycle time and thus influences vibration attenuation (i.e., downshifting or spectrum narrowing), which constitutes a form of tuning Further, vibration dampers in alternative tunable check valve assembly embodiments may comprise spring-mass combinations having discrete mechanical components in addition to, or in place of, viscoelastic and/or shear-thickening components. An example of such a spring-mass combination within a valve body central reservoir is schematically illustrated herein. 
     The second tunable component described herein is a tunable valve seat, certain embodiments of which may be employed with a conventional valve body or, alternatively, may be combined with a tunable check valve assembly to form a tunable check valve. A tunable valve seat in a fluid end for high pressure pumping comprises a concave mating surface and/or a lateral support assembly longitudinally spaced apart from a mating surface. A lateral support assembly, when present, is adjustably secured (e.g., on a lateral support mounting surface) or otherwise coupled to the mating surface. A lateral support assembly is a tunable structural feature for resiliently coupling the tunable valve seat to a fluid end housing (and thus damping vibrations therein). That is, a lateral support assembly (and thus a tunable valve seat of which it is a part) has at least one tunable valve seat resonant frequency similar to at least one fluid end resonant frequency. Further, a lateral support assembly may be combined with a concave mating surface to provide two tunable structural features in a single tunable valve seat. Tunability of the concave mating surface inheres in its influence on rebound cycle time through the predetermined orientation and degree of curvature of the concave mating surface. Since it constitutes a tunable structural feature, a concave mating surface may be present in a tunable valve seat without a lateral support assembly. In the latter case, the concave mating surface will be longitudinally spaced apart from a pump housing interface surface, rather than a lateral support mounting surface (examples of these two surfaces are schematically illustrated herein). In light of a tunable valve seat&#39;s potential for embodying either one or two tunable structural features, a plurality of tunable valve seat resonant frequencies may characterize a single tunable valve seat, with the respective frequencies being chosen in light of the fluid end resonance(s) and the valve closure impulse vibration spectrum. 
     Flexibility in the choice of tunable seat resonant frequencies is guided by optimization criteria for vibration control in a tunable fluid end. Such criteria will suggest specifics of a lateral support assembly&#39;s structure and/or the concave curvature of a mating surface. For example, a support assembly&#39;s one or more suitably-secured circular viscoelastic support elements comprise a highly adaptable support assembly design for resiliently coupling the tunable valve seat to a fluid end housing (and thus damping vibrations therein). At least one such viscoelastic support element comprises a support circumferential tubular area. And each support circumferential tubular area, in turn, comprises at least one shear thickening material having (i.e., being tuned to a resonance frequency similar to) at least one seat resonant frequency that may be chosen to be similar to at least one fluid end resonant frequency. As above, the choice of tuning frequency or frequencies for a tunable valve seat is not fixed, but is based on a predetermined optimization strategy for vibration damping in each fluid end 
     Note that in addition to individual tuning of a tunable check valve assembly and a tunable valve seat (forming a tunable check valve), the combination may be tuned as a whole. For example, a tunable check valve in a fluid end for high pressure pumping may alternatively or additionally be tuned for spectrum narrowing by ensuring that its rebound characteristic frequency (i.e., a function of rebound cycle time) is less than at least one fluid end resonant frequency. In such a case, for example, at least one tunable valve seat resonant frequency may be similar to at least one fluid end resonant frequency. 
     The third tunable component described herein is a tunable radial array disposed in a valve body. In a schematically illustrated embodiment, the valve body comprises guide means, a peripheral valve seat interface, and a fenestrated peripheral groove spaced radially apart from a central reservoir. A viscoelastic body element disposed in the groove (the groove element) is coupled to a viscoelastic body element disposed in the reservoir (the reservoir element) by a plurality of viscoelastic radial tension members passing through a plurality of fenestrations in the peripheral groove. Each radial tension member comprises at least one polymer composite and functions to couple the groove element with the reservoir element, a baseline level of radial tension typically arising due to shrinkage of the viscoelastic elements during curing. The tensioned radial members, as schematically illustrated herein, assist anchoring of the coupled groove element firmly within the peripheral seal-retention groove without the use of adhesives and/or serrations as have been commonly used in anchoring conventional valve seals. Radial tension members also create a damped resilient linkage of groove element to reservoir element (analogous in function to a spring-mass damper linkage). This damped linkage can be “tuned” to approximate (i.e., have a resonance similar to) one or more critical frequencies via choice of the viscoelastic and/or composite materials in the damped linkage. Note that radial tension members also furnish a transverse preload force on the valve body, thereby altering longitudinal compliance, rebound cycle time (and thus rebound characteristic frequency), and vibration attenuation. 
     The fourth tunable component described herein is a tunable plunger seal comprising at least one lateral support assembly (analogous to that of a tunable valve seat) securably and sealingly positionable along a plunger (e.g., in at least one packing box or analogous structure). The tunable plunger seal&#39;s lateral support assembly is analogous in structure and function to that of a tunable valve seat, as are the tuning procedures described above. 
     Note that the predetermined resonant frequency of each circular viscoelastic element of a lateral support assembly is affected by the viscoelastic material(s) comprising it, as well as by constraints imposed via adjacent structures (e.g., portions of a valve seat, fluid end housing, packing box or plunger). The choice of a variety of viscoelastic element inclusions includes, for example, reinforcing fibers, circumferential and/or central cavities within the viscoelastic element, and distributions of special-purpose materials (e.g., shear-thickening materials and/or graphene) within or in association with one or more viscoelastic elements. 
     Note also that the lateral support assembly of either a tunable valve seat or a tunable plunger seal resiliently links the respective valve seat or plunger with adjacent portions of a fluid end housing, effectively creating a spring-mass damper coupled to the housing. This damped linkage can be “tuned” to approximate one or more critical frequencies via, e.g., shear-thickening materials in the respective circumferential tubular areas as described herein. 
     Analogous damped linkages between the housing and one or more auxiliary masses may be incorporated in tunable fluid end embodiments for supplemental vibration damping at one or more fluid end resonant frequencies (e.g., auxiliary tuned vibration absorbers and/or tuned-mass dampers). Additionally or alternatively, one or more damping surface layers (applied, e.g., as metallic, ceramic and/or metallic/ceramic coatings) may be employed for dissipating vibration and/or for modifying one or more fluid end resonant frequencies in pursuit of an overall optimization plan for fluid end vibration control. Such damping surface layers may be applied to fluid ends by various methods known to those skilled in the art. These methods may include, for example, cathodic arc, pulsed electron beam physical vapor deposition (EB-PVD), slurry deposition, electrolytic deposition, sol-gel deposition, spinning, thermal spray deposition such as high velocity oxy-fuel (HVOF), vacuum plasma spray (VPS) and air plasma spray (APS). The surface layers may be applied to the desired fluid end surfaces in their entirety or applied only to specified areas. Each surface layer may comprise a plurality of sublayers, at least one of which may comprise, for example, titanium, nickel, cobalt, iron, chromium, silicon, germanium, platinum, palladium and/or ruthenium. An additional sublayer may comprise, for example, aluminum, titanium, nickel, chromium, iron, platinum, palladium and/or ruthenium. One or more sublayers may also comprise, for example, metal oxide (e.g., zirconium oxide and/or aluminum oxide) and/or a nickel-based, cobalt-based or iron-based superalloy. (See e.g., U.S. Pat. No. 8,591,196 B2, incorporated by reference). 
     Further as noted above, constraints on viscoelastic elements due to adjacent structures can function as a control mechanism by altering tunable component resonant frequencies. Examples of such effects are seen in embodiments comprising an adjustable flange coupled to the valve body for imposing a predetermined shear preload by further constraining a viscoelastic element already partially constrained in the reservoir. One or more tunable check valve assembly resonant frequencies may thus be predictably altered. Consequently, the associated valve-generated vibration spectrum transmissible to a housing may be narrowed, and its amplitude reduced, through hysteresis loss of valve-closure impulse energy at each predetermined assembly resonant frequency (e.g., by conversion of valve-closure impulse energy to heat energy, rather than vibration energy). 
     In addition to composite viscoelastic element inclusions, control mechanisms for alteration of tunable component resonant frequencies further include the number, size and spacing of peripheral groove fenestrations. When fenestrations are present, they increase valve assembly responsiveness to longitudinal compressive force while stabilizing viscoelastic and/or composite peripheral groove elements. Such responsiveness includes, but is not limited to, variations in the width of the peripheral groove which facilitate “tuning” of the groove together with its viscoelastic element(s). 
     Briefly summarizing, each embodiment of a tunable component attenuates and/or damps valve-generated vibration at one or more fluid end critical frequencies. The transmitted vibration spectrum is thus narrowed and its amplitude reduced through conversion and dissipation of valve-closure impulse (kinetic) energy as heat. One or more tunable component structural features are thus tunable to one or more frequencies similar to at least one fluid end resonant frequency to facilitate redistribution/dissipation of impulse kinetic energy, following its conversion to heat energy. 
     Continuing in greater detail, valve-closure impulse energy conversion in a tunable component primarily arises from hysteresis loss (e.g., heat loss) in viscoelastic and/or discrete-mechanical elements, but may also occur in related structures (e.g., in the valve body itself). Hysteresis loss in a particular structural feature is related in-part to that feature&#39;s compliance (i.e., the feature&#39;s structural distortion as a function of applied force). 
     Compliance arises in structural features of a tunable component, such as one or more viscoelastic elements, plus at least one other compliant portion. For example, a tunable check valve body distorts substantially elastically under the influence of a closing energy impulse, and its associated viscoelastic element(s) simultaneously experience(s) shear stress in accommodating the distortion. The resulting viscoelastic shear strain, however, is at least partially time-delayed. And the time delay introduces a phase-shift useful in damping valve-generated vibration (i.e., reducing its amplitude). Analogous time-delay phase shift occurs in a mass-spring damper comprising discrete mechanical elements. 
     In addition to vibration damping, a complementary function of a tunable component is narrowing of the spectrum of valve-generated vibration. Spectrum narrowing (or vibration down-shifting) is associated with compliance in the form of deformation over time in response to an applied force. Since each instance of compliance takes place over a finite time interval, the duration of a closing energy impulse is effectively increased (and the vibration spectrum correspondingly narrowed) as a function of compliance. 
     A narrowed valve-generated vibration spectrum, in turn, is less likely to generate destructive sympathetic vibration in adjacent regions of a fluid end housing. For this reason, compliant portions of a valve body are designed to elastically distort under the influence of the closing energy impulse (in contrast to earlier substantially-rigid valve designs). Compliance-related distortions are prominent in, but not limited to, the shapes of both the (peripheral) groove and the (relatively central) reservoir. Viscoelastic elements in the groove and reservoir resist (and therefore slow) the distortions, thus tending to beneficially increase the closing energy impulse&#39;s duration while narrowing the corresponding vibration spectrum. 
     Distortions of both groove and reservoir viscoelastic body elements result in viscoelastic stress and its associated time-dependent strain. But the mechanisms differ in the underlying distortions. In a peripheral groove, for example, proximal and distal groove walls respond differently to longitudinal compressive force on the tunable check valve assembly. They generally move out-of-phase longitudinally, thereby imposing time-varying compressive loads on the groove viscoelastic element. Thus the shape of the groove (and the overall compliance of the groove and its viscoelastic element) changes with time, making the groove as a whole responsive to longitudinal force on the assembly. 
     Peripheral groove fenestrations increase groove responsiveness to longitudinal force. As schematically illustrated herein, fenestrations increase groove responsiveness by changing the coupling of the proximal groove wall to the remainder of the valve body (see Detailed Description herein). 
     In the reservoir, in contrast, responsiveness to longitudinal force may be modulated by an adjustable preload flange centrally coupled to the valve body. 
     The flange imposes a shear preload on the viscoelastic reservoir element (i.e., shear in addition to that imposed by the reservoir itself and/or by the closing energy impulse acting on the viscoelastic element via the pumped fluid). The amount of shear preload varies with the (adjustable) radial and longitudinal positions of the flange within the reservoir. The overall compliance and resonances of the reservoir and its viscoelastic element may be predictably altered by such a shear preload, which is imposed by the flange&#39;s partial constraint of the viscoelastic reservoir element. Note that when reservoir and groove viscoelastic body elements are coupled by a plurality of radial tension members, as in a tunable radial array, the radial tension members lying in groove wall fenestrations allow transmission of shear stress between the groove and reservoir viscoelastic elements. 
     Thus, in tunable radial array embodiments, at least a first predetermined resonant frequency may substantially replicate a (similar) pump housing resonant frequency via adjustment of shear preload on the reservoir viscoelastic element. The plurality of fenestration elements coupling the reservoir element with the groove element may have at least a second predetermined resonant frequency related to the first predetermined resonant frequency and optionally achieved through choice of tensile strength of the radial tension members (i.e., fenestration elements). And at least a third predetermined resonant frequency related to the first and second predetermined resonant frequencies may be achieved through choice of at least one shear thickening material in circumferential tubular areas of the groove viscoelastic element and/or one or more support circumferential tubular areas. 
     Note that any structural feature of a tunable check valve assembly or tunable radial array (e.g., a valve body or a viscoelastic element) may be supplemented with one or more reinforcement components to form a composite feature. Reinforcement materials tend to alter compliance and may comprise, for example, a flexible fibrous material (e.g., carbon nanotubes, graphene), a shear-thickening material, and/or other materials as described herein. 
     As noted above, alterations in compliance (with its associated hysteresis loss) contribute to predetermined vibration spectrum narrowing. Such compliance changes (i.e., changes in displacement as a function of force) may be achieved through adjustment of constraint. Constraint, in turn, may be achieved, e.g., via compression applied substantially longitudinally by the adjustable preload flange to a constrained area of the viscoelastic reservoir element. In embodiments comprising a central longitudinal guide stem, the constrained area may be annular. And adjacent to such an annular constrained area may be another annular area of the viscoelastic reservoir element which is not in contact with the adjustable preload flange (i.e., an annular unconstrained area). This annular unconstrained area is typically open to pumped fluid pressure. 
     Preload flange adjustment may change the longitudinal compliance of the tunable check valve assembly by changing the effective flange radius and/or the longitudinal position of the flange as it constrains the viscoelastic reservoir element. Effective flange radius will generally exceed actual flange radius due to slowing of (viscous) viscoelastic flow near the flange edge. This allows tuning of the check valve assembly to a first predetermined assembly resonant frequency for maximizing hysteresis loss. Stated another way, by constraining a vibrating structure (e.g., an area of the viscoelastic reservoir element), it is possible to force the vibrational energy into different modes and/or frequencies. See, e.g., U.S. Pat. No. 4,181,027, incorporated by reference. 
     The invention thus includes means for constraining one or more separate viscoelastic elements of a valve assembly, as well as means for constraining a plurality of areas of a single viscoelastic element. And such constraint may be substantially constant or time-varying, with correspondingly different effects on resonant frequencies. Peripherally, time-varying viscoelastic element constraint may be provided by out-of-phase longitudinal movement of peripheral groove walls. In contrast, time-varying viscoelastic element constraint may be applied centrally by a flange coupled to the valve body. 
     Flange radial adjustment is facilitated, e.g., via a choice among effective flange radii and/or flange periphery configurations (e.g., cylindrical or non-cylindrical). Flange longitudinal movement may be adjusted, for example, by (1) use of mechanical screws or springs, (2) actuation via pneumatic, hydraulic or electrostrictive transducers, or (3) heat-mediated expansion or contraction. Flange longitudinal movement may thus be designed to be responsive to operational pump parameters such as temperature, acceleration, or pressure. Since pump housing resonant frequencies may also respond to such parameters, tunable check valve assemblies and tunable check valves may be made at least partially self-adjusting (i.e., operationally adaptive or auto-adjusting) so as to change their energy-absorbing and spectrum-narrowing characteristics to optimally extend pump service life. 
     Note that in certain embodiments, the preload flange may comprise a substantially cylindrical periphery associated with substantially longitudinal shear. Other embodiments may comprise a non-cylindrical periphery for facilitating annular shear preload having both longitudinal and transverse components associated with viscoelastic flow past the flange. Such an invention embodiment provides for damping of transverse as well as longitudinal vibration. Transverse vibration may originate, for example, when slight valve body misalignment with a valve seat causes abrupt lateral valve body movement during valve closing. 
     Note also that one or more flanges may or may not be longitudinally fixed to the guide stem for achieving one or more predetermined assembly resonant frequencies. 
     And note further that the first predetermined assembly resonant frequency of greatest interest, of course, will typically approximate one of the natural resonances of the pump and/or pump housing. Complementary hysteresis loss and vibration spectrum narrowing may be added via a second predetermined assembly resonant frequency achieved via the viscoelastic groove element (which may comprise at least one circumferential tubular area containing at least one shear-thickening material). The time-varying viscosity of the shear-thickening material(s), if present, furnishes a non-linear constraint of the vibrating structure analogous in part to that provided by the adjustable preload flange. The result is a predetermined shift of the tunable check valve assembly&#39;s vibrating mode analogous to that described above. 
     Note that when a nonlinear system is driven by a periodic function, such as can occur with harmonic excitation, chaotic dynamic behavior is possible. Depending on the nature of the nonlinear system, as well as the frequency and amplitude of the driving force, the chaotic behavior may comprise periodic oscillations, almost periodic oscillations, and/or coexisting (multistable) periodic oscillations and nonperiodic-nonstable trajectories (see  Harris , p. 4-28). 
     In addition to a shift in the tunable check valve assembly&#39;s vibrating mode, incorporation of at least one circumferential tubular area containing at least one shear-thickening material within the viscoelastic groove element increases impulse duration by slightly slowing valve closure due to reinforcement of the viscoelastic groove element. Increased impulse duration, in turn, narrows the closing energy impulse vibration spectrum. And shear-thickening material itself is effectively constrained by its circumferential location within the viscoelastic groove element(s). 
     The shear-thickening material (sometimes termed dilatant material) is relatively stiff near the time of impact and relatively fluid at other times. Since the viscoelastic groove element strikes a valve seat before the valve body, complete valve closure is slightly delayed by the shear-thickening action. The delay effectively increases the valve-closure energy impulse&#39;s duration, which means that vibration which is transmitted from the tunable check valve assembly to its (optionally tunable) valve seat and pump housing has a relatively narrower spectrum and is less likely to excite vibrations that predispose a pump housing to early fatigue failure. The degree of spectrum narrowing can be tuned to minimize excitation of known pump housing resonances by appropriate choice of the shear-thickening material. Such vibration attenuation, and the associated reductions in metal fatigue and corrosion susceptibility, are especially beneficial in cases where the fluid being pumped is corrosive. 
     The functions of the viscoelastic groove element, with its circumferential shear-thickening material, are thus seen to include those of a conventional valve seal as well as those of a tunable vibration attenuator and a tunable vibration damper. See, e.g., U.S. Pat. No. 6,026,776, incorporated by reference. Further, the viscoelastic reservoir element, functioning with a predetermined annular shear preload provided via an adjustable preload flange, can dissipate an additional portion of valve-closure impulse energy as heat while also attenuating and damping vibration. And viscoelastic fenestration elements, when present, may contribute further to hysteresis loss as they elastically retain the groove element in the seal-retention groove via coupling to the reservoir element. Overall hysteresis loss in the viscoelastic elements combines with hysteresis loss in the valve body to selectively reduce the bandwidth, amplitude and duration of vibrations that the closing impulse energy would otherwise tend to excite in the valve and/or pump housing. 
     Examples of mechanisms for such selective vibration reductions are seen in the interactions of the viscoelastic reservoir element with the adjustable preload flange. The interactions contribute to hysteresis loss in a tunable check valve assembly by, for example, creating what has been termed shear damping (see, e.g., U.S. Pat. No. 5,670,006, incorporated by reference). With the preload flange adjustably fixed centrally to the check valve body (e.g., fixed to a central guide stem), valve-closure impact causes both the preload flange and guide stem to temporarily move distally with respect to the (peripheral) valve seat interface (i.e., the valve body experiences a concave-shaped flexure). The impact energy associated with valve closure causes temporary deformation of the check valve body; that is, the valve body periphery (e.g., the valve seat interface) is stopped by contact with a valve seat while the central portion of the valve body continues (under inertial forces and pumped-fluid pressure) to elastically move distally. Thus, the annular constrained area of the viscoelastic reservoir element (shown constrained by the preload flange in the schematic illustrations herein) moves substantially countercurrent (i.e., in shear) relative to the annular unconstrained area (shown radially farther from the guide stem and peripheral to the preload flange). That is, relative distal movement of the preload flange thus tends to extrude the (more peripheral) annular unconstrained area proximally. Energy lost (i.e., dissipated) in connection with the resulting shear strain in the viscoelastic element is subtracted from the total closing impulse energy otherwise available to excite destructive flow-induced vibration resonances in a valve, valve seat and/or pump housing. See, e.g., U.S. Pat. No. 5,158,162, incorporated by reference. 
     Note that in viscoelastic and shear-thickening materials, the relationship between stress and strain (and thus the effect of material constraint on resonant frequency) is generally time-dependent and non-linear. So a desired degree of non-linearity in “tuning” may be predetermined by appropriate choice of viscoelastic and shear-thickening materials in a tunable check valve assembly or tunable check valve. 
     Another aspect of the interaction of the viscoelastic reservoir element with an adjustable preload flange contributes to vibration damping and/or absorption in a tunable check valve assembly. As a result of compliance in the viscoelastic element, longitudinal movement of a guide stem and a coupled preload flange results in a phase lag as shear stress develops within the viscoelastic material. This is analogous to the phase lag seen in the outer ring movement in an automotive torsional vibration damper or the antiphase movement of small masses in an automotive pendulum vibration damper. See, e.g., the &#39;776 patent cited above. Adjusting the shear preload flange as described above effectively changes the tunable check valve assembly&#39;s compliance and thus the degree of phase lag. One may thus, in one or more limited operational ranges, tune viscoelastic element preload to achieve effective vibration damping plus dynamic vibration absorption at specific frequencies of interest (e.g., pump housing resonant frequencies). 
     To achieve the desired hysteresis loss associated with attenuation and vibration damping effects described herein, different viscoelastic and/or composite elements may be constructed to have specific elastic and/or viscoelastic properties. Note that the term elastic herein implies substantial characterization by a storage modulus, whereas the term viscoelastic herein implies substantial characterization by a storage modulus and a loss modulus. See, e.g., the &#39;006 patent cited above. 
     Specific desired properties for each viscoelastic element arise from a design concept requiring coordinated functions depending on the location of each element. The viscoelastic reservoir element affects hysteresis associated with longitudinal compliance of the tunable check valve assembly because it viscoelasticly accommodates longitudinal deformation of the valve body toward a concave shape. Hysteresis in the viscoelastic groove element (related, e.g., to its valve seal and vibration damping functions) and the valve body itself further reduces closing energy impulse amplitude through dissipation of portions of closing impulse energy as heat. 
     Elastic longitudinal compliance of a tunable check valve assembly results in part from elastic properties of the materials comprising the tunable check valve assembly. Such elastic properties may be achieved through use of composites comprising reinforcement materials as, for example, in an elastic valve body comprising steel, carbon fiber reinforced polymer, carbon nanotube/graphene reinforced polymer, and/or carbon nanotube/graphene reinforced metal matrix. The polymer may comprise a polyaryletherketone (PAEK), for example, polyetheretherketone (PEEK). See, e.g., U.S. Pat. No. 7,847,057 B2, incorporated by reference. 
     Note that the description herein of valve body flexure as concave-shaped refers to a view from the proximal or high-pressure side of the valve body. Such flexure is substantially elastic and may be associated with slight circular rotation (i.e., a circular rolling contact) of the valve body&#39;s valve seat interface with the valve seat itself. When the degree of rolling contact is sufficient to justify conversion of the valve seat interface from a conventional frusto-conical shape to a convex curved shape (which may include, e.g., circular, elliptic and/or parabolic portions), a curved concave tunable valve seat mating surface may be used. In such cases, the valve seat interface has correspondingly greater curvature than the concave tunable valve seat mating surface (see Detailed Description herein). Such rolling contact, when present, augments elastic formation of the concave valve body flexure on the pump pressure stroke, reversing the process on the suction stroke. 
     The circular rolling contact described herein may be visualized by considering the behavior of the convex valve seat interface as the valve body experiences concave flexure (i.e., the transformation from a relatively flat shape to a concave shape). During such flexure the periphery of the valve seat interface rotates slightly inwardly and translates slightly proximally (relative to the valve body&#39;s center of gravity) to become the proximal rim of the concave-shaped flexure. 
     While substantially elastic, each such valve body flexure is associated with energy loss from the closing energy impulse due to hysteresis in the valve body. Frictional heat loss (and any wear secondary to friction) associated with any circular rolling contact of the convex valve seat interface with the concave tunable valve seat mating surface is intentionally relatively low. Thus, the rolling action, when present, minimizes wear that might otherwise be associated with substantially sliding contact of these surfaces. Further, when rolling contact between valve body and tunable valve seat is present during both longitudinal valve body flexure and the elastic rebound which follows, trapping of particulate matter from the pumped fluid between the rolling surfaces tends to be minimized. 
     Since rolling contact takes place over a finite time interval, it also assists in smoothly redirecting pumped fluid momentum laterally and proximally. Forces due to oppositely directed radial components of the resultant fluid flow tend to cancel, and energy lost in pumped fluid turbulence is subtracted (as heat) from that of the valve-closure energy impulse, thus decreasing both its amplitude and the amplitude of associated vibration. 
     In addition to the above described energy dissipation (associated with hysteresis secondary to valve body flexure), hysteresis loss will also occur during pressure-induced movements of the viscoelastic groove element (in association with the valve seal function). Note that pumped fluid pressure acting on a valve comprising an embodiment of the invention&#39;s tunable check valve assembly may hydraulically pressurize substantially all of the viscoelastic elements in a tunable check valve assembly. Although polymers suitable for use in the viscoelastic elements generally are relatively stiff at room ambient pressures and temperatures, the higher pressures and temperatures experienced during pump pressure strokes tend to cause even relatively stiff polymers to behave like fluids which can transmit pressure hydraulically. Thus, a viscoelastic element in a peripheral seal-retention groove is periodically hydraulically pressurized, thereby increasing its sealing function during the high-pressure portion of the pump cycle. Hydraulic pressurization of the same viscoelastic element is reduced during the low-pressure portion of the pump cycle when the sealing function is not needed. 
     Because of the above-described energy loss and the time required for valve body longitudinal deformation to take place, with the associated dissipation of closing impulse energy described above, a valve-closure energy impulse applied to a tunable check valve assembly or tunable radial array is relatively lower in amplitude and longer in duration (e.g., secondary to having a longer rise time) than an analogous valve-closure energy impulse applied to a conventionally stiff valve body which closes on a conventional frusto-conical valve seat. The combination of lower amplitude and increased duration of the valve-closure energy impulse results in a narrowed characteristic vibration bandwidth having reduced potential for induction of damaging resonances in the valve, valve seat, and adjacent portions of the pump housing. See, e.g., the above-cited &#39;242 patent. 
     Note that in describing the fluid-like behavior of certain polymers herein under elevated heat and pressure, the term “polymer” includes relatively homogenous materials (e.g., a single-species fluid polymer) as well as composites and combination materials containing one or more of such relatively homogenous materials plus finely divided particulate matter (e.g., nanoparticles) and/or other dispersed species (e.g., species in colloidal suspension, graphene) to improve heat scavenging and/or other properties. See, e.g., U.S. Pat. No. 6,432,320 B1, incorporated by reference. 
     In addition to heat scavenging, damping is a function of the viscoelastic elements in various embodiments of the invention. Optimal damping is associated with relatively high storage modulus and loss tangent values, and is obtained over various temperature ranges in multicomponent systems described as having macroscopically phase-separated morphology, microheterogeneous morphology, and/or at least one interpenetrating polymer network. See, e.g., the above-cited &#39;006 patent and U.S. Pat. Nos. 5,091,455; 5,238,744; 6,331,578 B1; and 7,429,220 B2, all incorporated by reference. 
     Summarizing salient points of the above description, recall that vibration attenuation and damping in a tunable check valve assembly, tunable valve seat, tunable plunger seal, or tunable radial array of the invention operate via four interacting mechanisms. First, impulse amplitude is reduced by converting a portion of total closing impulse energy to heat (e.g., via hysteresis and fluid turbulence), which is then ultimately rejected to the check valve body surroundings (e.g., the pumped fluid). Each such reduction of impulse amplitude means lower amplitudes in the characteristic vibration spectrum transmitted to the pump housing. 
     Second, the closing energy impulse as sensed at the valve seat is reshaped in part by lengthening the rebound cycle time (estimated as the total time associated with peripheral valve seal compression, concave valve body flexure and elastic rebound). Such reshaping may in general be accomplished using mechanical/hydraulic/pneumatic analogs of electronic wave-shaping techniques. In particular, lengthened rebound cycle time is substantially influenced by the valve body&#39;s increased longitudinal compliance associated with the rolling contact/seal and concave valve body flexure described herein between valve body and valve seat. The units of lengthened cycle times are seconds, so their inverse functions have dimensions of per second (or 1/sec), the same dimensions as frequency. Thus, as noted above, the inverse function is termed herein rebound characteristic frequency. 
     Lowered rebound characteristic frequency (i.e., increased rebound cycle time) corresponds to slower rebound, with a corresponding reduction of the impulse&#39;s characteristic bandwidth due to loss of higher frequency content. This condition is created during impulse hammer testing by adding to hammer head inertia and by use of softer impact tips (e.g., plastic tips instead of the metal tips used when higher frequency excitation is desired). In contrast, tunable check valve assemblies and tunable radial arrays achieve bandwidth narrowing (and thus reduction of the damage potential of induced higher-frequency vibrations) at least in part through increased longitudinal compliance. In other words, bandwidth narrowing is achieved in embodiments of the invention through an increase of the effective impulse duration (as by, e.g., slowing the impulse&#39;s rise time and/or fall time as the valve assembly&#39;s components flex and relax over a finite time interval). 
     Third, induced vibration resonances of the tunable check valve assembly, tunable valve seat, and/or other tunable components are effectively damped by interactions generating structural hysteresis loss. Associated fluid turbulence further assists in dissipating heat energy via the pumped fluid. 
     And fourth, the potential for excitation of damaging resonances in pump vibration induced by a closing energy impulse is further reduced through narrowing of the impulse&#39;s characteristic vibration bandwidth by increasing the check valve body&#39;s effective inertia without increasing its actual mass. Such an increase of effective inertia is possible because a portion of pumped fluid moves with the valve body as it flexes and/or longitudinally compresses. The mass of this portion of pumped fluid is effectively added to the valve body&#39;s mass during the period of flexure/relaxation, thereby increasing the valve body&#39;s effective inertia to create a low-pass filter effect (i.e., tending to block higher frequencies in the manner of an engine mount). 
     To increase understanding of the invention, certain aspects of tunable components (e.g., alternate embodiments and multiple functions of structural features) are considered in greater detail. Alternate embodiments are available, for example, in guide means known to those skilled in the art for maintaining valve body alignment within a (suction or discharge) bore. Guide means thus include, e.g., a central guide stem and/or a full-open or wing-guided design (i.e., having a distal crow-foot guide). 
     Similarly, alteration of a viscoelastic element&#39;s vibration pattern(s) in a tunable fluid end is addressed (i.e., tuned) via adjustable and/or time-varying constraints. Magnitude and timing of the constraints are determined in part by closing-impulse-related distortions and/or the associated vibration. For example, a viscoelastic reservoir (or central) element is at least partially constrained as it is disposed in the central annular reservoir, an unconstrained area optionally being open to pumped fluid pressure. That is, the viscoelastic reservoir element is at least partially constrained by relative movement of the interior surface(s) of the (optionally annular) reservoir, and further constrained by one or more structures (e.g., flanges) coupled to such surface(s). Analogously, a viscoelastic groove (or peripheral) element is at least partially constrained by relative movement of the groove walls, and further constrained by shear-thickening material within one or more circumferential tubular areas of the element (any of which may comprise a plurality of lumens). 
     Since the magnitude and timing of closing-impulse-related distortions are directly related to each closing energy impulse, the tunable fluid end&#39;s overall response is adaptive to changing pump operating pressures and speeds on a stroke-by-stroke basis. So for each set of operating parameters (i.e., for each pressure/suction stroke cycle), one or more of the constrained viscoelastic elements has at least a first predetermined assembly resonant frequency substantially similar to an instantaneous pump resonant frequency (e.g., a resonant frequency measured or estimated proximate the suction valve seat deck). And for optimal damping, one or more of the constrained viscoelastic elements may have, for example, at least a second predetermined assembly resonant frequency similar to the first predetermined assembly resonant frequency. 
     Note that the adaptive behavior of viscoelastic elements is beneficially designed to complement both the time-varying behavior of valves generating vibration with each punp pressure stroke, and the time-varying response of the fluid end as a whole to that vibration. 
     Note also that a tunable check valve assembly and/or tunable valve seat analogous to those designed for use in a tunable suction check valve may be incorporated in a tunable discharge check valve as well. Either a tunable suction check valve or a tunable discharge check valve or both may be installed in a pump fluid end housing. Additionally, one or more other tunable components may be combined with tunable suction and/or discharge check valves. A pump housing resonant frequency may be chosen as substantially equal to a first predetermined resonant frequency of each of the tunable components installed, or of any combination of the installed tunable components. Or the predetermined component resonant frequencies may be tuned to approximate different pump housing resonant frequencies as determined for optimal vibration damping. 
     For increased flexibility in accomplishing the above tuning, fenestrations may be present in the groove wall to accommodate radial tension members. At least a portion of each fenestration may have a transverse area which increases with decreasing radial distance to said longitudinal axis. That is, each fenestration flares to greater transverse areas in portions closer to the longitudinal axis, relative to the transverse areas of portions of the fenestration which are more distant from the longitudinal axis. Thus, a flared fenestration is partly analogous to a conventionally flared tube, with possible differences arising from the facts that (1) fenestrations are not limited to circular cross-sections, and (2) the degree of flare may differ in different portions of a fenestration. Such flares assist in stabilizing a viscoelastic groove element via a plurality of radial tension members. 
     Note that in addition to the example alternate embodiments described herein, still other alternative invention embodiments exist, including valves, pump housings and pumps comprising one or more of the example embodiments or equivalents thereof. Additionally, use of a variety of fabrication techniques known to those skilled in the art may lead to embodiments differing in detail from those schematically illustrated herein. For example, internal valve body spaces may be formed during fabrication by welding (e.g., inertial welding or laser welding) valve body portions together as in the above-cited &#39;837 patent, or by separately machining such spaces with separate coverings. Valve body fabrication may also be by rapid-prototyping (i.e., layer-wise) techniques. See, e.g., the above-cited &#39;057 patent. Viscoelastic elements may be cast and cured separately or in place in a valve body as described herein. See, e.g., U.S. Pat. No. 7,513,483 B1, incorporated by reference. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic 3-dimensional view of a partially sectioned tunable check valve assembly/tunable radial array embodiment showing how an adjustable preload flange constrains an area of the viscoelastic reservoir element as described herein. 
         FIG. 2  includes a schematic 3-dimensional exploded view of the tunable check valve assembly/tunable radial array embodiment of  FIG. 1  showing viscoelastic body elements, the valve body, and the adjustable preload flange. 
         FIG. 3  is a schematic 3-dimensional partially-sectioned view of viscoelastic reservoir, groove and fenestration elements (i.e., viscoelastic body elements) of  FIGS. 1 and 2  showing the constrained area of the reservoir element where it contacts an adjustable preload flange, as well as an adjacent unconstrained area. 
         FIG. 4  is a schematic 3-dimensional partially-sectioned view of two check valve bodies with an adjustable preload flange located at different longitudinal positions on a central guide stem. 
         FIG. 5  is a schematic 3-dimensional instantaneous partially-sectioned view of shear-thickening material which would, e.g., substantially fill a circumferential tubular area in the viscoelastic groove element and/or a support circumferential tubular area of a tunable valve seat or a tunable plunger seal. 
         FIG. 6  is a schematic illustration of an exploded partially-sectioned 2-dimensional view of major components of a pump fluid end subassembly, together with brief explanatory comments on component functions. The schematically-illustrated subassembly comprises a pumping chamber within a subassembly pump housing, the pumping chamber being in fluid communication with a suction bore, a discharge bore, and a piston/plunger bore. Schematic representations of a suction check valve, a discharge check valve, and a piston/plunger are shown in their respective bores, together with brief annotations and graphical aids outlining the structural relationships. 
         FIG. 7  is a schematic illustration of two views of an exploded partially-sectioned 3-dimensional view of a valve body and tunable valve seat embodiment. Curved longitudinal section edges of the valve body&#39;s convex valve seat interface and corresponding concave mating portions of the tunable valve seat are shown schematically in detail to aid description herein of a rolling valve seal. A tunable (suction or discharge) check valve embodiment of the invention may comprise a combination of a tunable check valve assembly/tunable radial array (see, e.g.,  FIGS. 1 and 2 ) and a tunable valve seat (see, e.g.,  FIGS. 7 and 8 ). 
         FIG. 8  is a schematic 3-dimensional exploded and partially-sectioned view of a tunable valve seat embodiment showing a concave mating surface longitudinally spaced apart from a lateral support mounting surface, and an adjustable lateral support assembly comprising first and second securable end spacers in combination with a plurality of circular viscoelastic support elements, each support element comprising a support circumferential tubular area. 
         FIG. 9  is a schematic 3-dimensional exploded view of a partially sectioned tunable check valve assembly embodiment. A dilatant (i.e., shear-thickening) liquid is schematically shown being added to a check valve body&#39;s internal cavity, the cavity being shown as enclosing a tuned vibration damper comprising discrete mechanical elements (e.g., a mass and three springs). 
         FIG. 10  is a schematic 3-dimensional exploded view of a tunable check valve embodiment comprising the tunable check valve assembly of  FIG. 9  together with a tunable valve seat, the tunable check valve embodiment including structures to facilitate a rolling seal between the valve body&#39;s valve seat interface and the tunable valve seat&#39;s mating surface. Note that the valve seat interface has correspondingly greater curvature than the mating surface, and the mating surface has correspondingly less curvature than the valve seat interface. 
         FIG. 11  is a schematic 3-dimensional exploded view of an alternate tunable check valve embodiment comprising the tunable check valve assembly of  FIG. 9  together with a tunable valve seat, the tunable check valve embodiment including structures to facilitate a rolling seal between the check valve body&#39;s peripheral valve seat interface and the tunable valve seat&#39;s mating surface. An adjustable lateral support assembly is shown with the tunable valve seat, the assembly comprising first and second securable end spacers in combination with a plurality of circular viscoelastic support elements, each support element comprising a support circumferential tubular area. 
     
    
    
     DETAILED DESCRIPTION 
     Tunable fluid end embodiments comprise a family, each family member comprising a fluid end housing with at least one installed tunable component chosen from: tunable check valve assemblies, tunable valve seats, tunable radial arrays and/or tunable plunger seals. Installing one or more tunable check valve assemblies, for example, facilitates selective attenuation of valve-generated vibration at its source. The likelihood of fluid end failures associated with fatigue cracking and/or corrosion fatigue is thereby reduced. Adding tunable valve seats, tunable radial arrays and/or plunger seals to tunable check valve assemblies in a fluid end further facilitates optimal damping and/or selective attenuation of vibration at one or more predetermined (and frequently-localized) fluid end resonant frequencies. Optimized vibration attenuation (via, e.g., optimized fluid end damping) is provided by altering resonant frequencies in each tunable component in relation to one or more (measured or estimated) fluid end resonant frequencies and/or tunable component resonant frequencies. 
     In general, a tunable (suction or discharge) check valve of the invention may comprise, for example, a combination of a tunable check valve assembly/tunable radial array  99  (see, e.g.,  FIG. 1 ) and a tunable valve seat  20  or a tunable valve seat  389  (see, e.g.,  FIGS. 7 and 11 ). Details of the structure and functions of each component are provided herein both separately and as combined with other components to obtain synergistic benefits contributing to longer pump service life. 
       FIGS. 1 and 2  schematically illustrate an invention embodiment of a tunable check valve assembly/tunable radial array  99  substantially symmetrical about a longitudinal axis. Illustrated components include a valve body  10 , an adjustable preload flange  30 , and a plurality of viscoelastic body elements  50 . Check valve body  10 , in turn, comprises a peripheral groove  12  (see  FIG. 2 ) spaced apart by an annular (central) reservoir  16  from a longitudinal guide stem  14 , groove  12  being responsive to longitudinal compressive force. A plurality of viscoelastic body elements  50  comprises an annular (central) reservoir element  52  coupled to a (peripheral) groove element  54  by a plurality of (optional) radial fenestration elements  56  (in fenestrations  18 ) to form a tunable radial array. Groove element  54  functions as a vibration damper and valve seal, comprising at least one circumferential tubular area  58 . 
     Responsiveness of groove  12  to longitudinal compressive force is characterized in part by damping of groove wall  11 / 13 / 15  vibrations. Such damping is due in part to out-of-phase vibrations in proximal groove wall  13  and distal groove wall  11  which are induced by longitudinal compressive force. Such out-of-phase vibrations will cause various groove-related dimensions to vary with longitudinal compressive force, thereby indicating the responsiveness of groove  12  to such force (see, for example, the dimension labeled A in  FIG. 2 ). Each phase shift, in turn, is associated with differences in the coupling of proximal groove wall  13  to guide stem  14  (indirectly via longitudinal groove wall  15  and radial reservoir floor  19 ) and the coupling of distal groove wall  11  to guide stem  14  (directly via radial reservoir floor  19 ). Note that longitudinal groove wall  15  may comprise fenestrations  18 , thereby increasing the responsiveness of groove  12  to longitudinal compressive force on tunable check valve assembly  99 . 
     Referring to  FIGS. 1-3 , adjustable preload flange  30  extends radially from guide stem  14  (toward peripheral reservoir wall  17 ) over, for example, about 20% to about 80% of viscoelastic reservoir element  52  (see  FIG. 3 ). Adjustable preload flange  30  thus imposes an adjustable annular shear preload over an annular constrained area  62  of viscoelastic reservoir element  52  to achieve at least a first predetermined assembly resonant frequency substantially replicating a (similar) measured or estimated resonant frequency (e.g., a pump housing resonant frequency). Note that an adjacent annular unconstrained area  60  of viscoelastic reservoir element  52  remains open to pumped fluid pressure. Note also that adjustable preload flange  30  may be adjusted in effective radial extent and/or longitudinal position. 
     Note further that annular constrained area  62  and annular unconstrained area  60  are substantially concentric and adjacent. Thus, for a tunable suction valve subject to longitudinal (i.e., distally-directed) compressive constraint applied via preload flange  30  to annular constrained area  62 , annular unconstrained area  60  will tend to move (i.e., extrude) proximally relative to area  62 . The oppositely-directed (i.e., countercurrent) movements of constrained and unconstrained annular areas of viscoelastic reservoir element  52  create a substantially annular area of shear stress. 
     Finally, each circumferential tubular area  58  is substantially filled with at least one shear-thickening material  80  (see  FIG. 5 ) chosen to achieve at least a second predetermined assembly resonant frequency similar, for example, to the first predetermined assembly resonant frequency). Note that  FIG. 5  schematically represents a partially-sectioned view of an instantaneous configuration of the shear-thickening material  80  within circumferential tubular area  58 . 
     Referring to  FIGS. 1 and 2  in greater detail, a tunable check valve assembly/tunable radial array embodiment  99  comprises viscoelastic body elements  50  which comprise, in turn, reservoir (central) element  52  coupled to groove (peripheral) element  54  via radial fenestration (tension) elements  56 . Elements  52 ,  54  and  56  are disposed in (i.e., integrated with and/or lie substantially in) reservoir  16 , groove  12  and fenestrations  18  respectively to provide a tuned radial array having at least a third predetermined resonant frequency. An adjustable preload flange  30  is coupled to guide stem  14  and contacts viscoelastic reservoir element  52  in reservoir  16  to impose an adjustable annular constraint on viscoelastic reservoir element  52  for achieving at least a first predetermined assembly resonant frequency substantially similar to, for example, a measured resonant frequency (e.g., a pump housing resonant frequency). Such adjustable annular constraint imposes an adjustable shear preload between constrained annular area  62  and unconstrained annular area  60 . Tunable check valve assembly  99  may additionally comprise at least one circumferential tubular area  58  in groove element  54  residing in groove  12 , each tubular area  58  being substantially filled with at least one shear-thickening material  80  chosen to achieve at least a second predetermined assembly resonant frequency similar, for example, to the first predetermined assembly resonant frequency). 
     The above embodiment may be installed in a pump housing having a measured housing resonant frequency; the measured housing resonant frequency may then be substantially replicated in the (similar) first predetermined resonant frequency of the tunable check valve assembly. Such a combination would be an application of an alternate embodiment. An analogous tuning procedure may be followed if the tunable check valve assembly of the second embodiment is installed in a pump having a (similar or different) resonant frequency substantially equal to the second predetermined resonant frequency. This synergistic combination would broaden the scope of the valve assembly&#39;s beneficial effects, being yet another application of the invention&#39;s alternate embodiment. 
     Note that preload flange  30  may have a non-cylindrical periphery  32  for imposing on viscoelastic reservoir element  52  an adjustable annular shear preload having both longitudinal and transverse components. 
     Note further that the periphery of adjustable preload flange  30 , if cylindrical, predisposes a tunable check valve assembly to substantially longitudinal shear damping with each longitudinal distortion of check valve body  10  associated with valve closure. The character of such shear damping depends, in part, on the longitudinal position of the preload flange. Examples of different longitudinal positions are seen in  FIG. 4 , which schematically illustrates the flange  30 ′ longitudinally displaced from flange  30 ″. Further, as shown in  FIG. 4 , the convex periphery of a longitudinally adjusted preload flange  30 ′ or  30 ″ may introduce shear damping of variable magnitude and having both longitudinal and transverse components. Such damping may be beneficial in cases where significant transverse valve-generated vibration occurs. 
     To clarify the placement of viscoelastic body elements  50 , labels indicating the portions are placed on a sectional view in  FIGS. 2 and 3 . Actual placement of viscoelastic body elements  50  in valve body  10  (see  FIG. 1 ) may be by, for example, casting viscoelastic body elements  50  in place, or placing viscoelastic body elements  50  (which have been precast) in place during layer-built or welded fabrication. The tunable check valve assembly embodiment of the invention is intended to represent check valve body  10  and viscoelastic body elements  50  as complementary components at any stage of manufacture leading to functional integration of the two components. 
     To enhance scavenging of heat due to friction loss and/or hysteresis loss, shear-thickening material  80  and/or viscoelastic body elements  50  may comprise one or more polymers which have been augmented with nanoparticles and/or graphene  82  (see, e.g.,  FIG. 5 ). Nanoparticles and/or graphene may be invisible to the eye as they are typically dispersed in a colloidal suspension. Hence, they are schematically represented by cross-hatching  82  in  FIG. 5 . Nanoparticles may comprise, for example, carbon forms (e.g., graphene) and/or metallic materials such as copper, beryllium, titanium, nickel, iron, alloys or blends thereof. The term nanoparticle may conveniently be defined as including particles having an average size of up to about 2000 nm. See, e.g., the &#39;320 patent. 
       FIG. 6  is a schematic illustration of an exploded partially-sectioned 2-dimensional view of major components of a pump fluid end subassembly  88 , together with graphical aids and brief explanatory comments on component functions. The schematically-illustrated subassembly  88  comprises a pumping chamber  74  within a subassembly (pump) housing  78 , the pumping chamber  74  being in fluid communication with a suction bore  76 , a discharge bore  72 , and a piston/plunger bore  70 . Note that piston/plunger bore  70  comprises at least one recess (analogous to that labeled “packing box” in  FIG. 6 ) in which at least one lateral support assembly  130  (see  FIG. 8 ) may be sealingly positionable along the plunger as part of a tunable plunger seal embodiment. Schematic representations of a tunable suction valve  95  (illustrated for simplicity as a hinged check valve), a tunable discharge valve  97  (also illustrated for simplicity as a hinged check valve), and a piston/plunger  93  (illustrated for simplicity as a plunger) are shown in their respective bores. Note that longitudinally-moving valve bodies in check valve embodiments schematically illustrated herein (e.g., valve body  10 ) are associated with certain operational phenomena analogous to phenomena seen in hinged check valves (including, e.g., structural compliance secondary to closing energy impulses). 
     Regarding the graphical aids of  FIG. 6 , the double-ended arrows that signify fluid communication between the bores (suction, discharge and piston/plunger) and the pumping chamber are double-ended to represent the fluid flow reversals that occur in each bore during each transition between pressure stroke and suction stroke of the piston/plunger. The large single-ended arrow within the pumping chamber is intended to represent the periodic and relatively large, substantially unidirectional fluid flow from suction bore through discharge bore during pump operation. 
     Further regarding the graphical aids of  FIG. 6 , tunable suction (check) valve  95  and tunable discharge (check) valve  97  are shown schematically as hinged check valves in  FIG. 6  because of the relative complexity of check valve embodiments having longitudinally-moving valve bodies. More detailed schematics of several check valve assemblies and elements are shown in  FIGS. 1-11 , certain tunable check valve embodiments comprising a tunable check valve assembly and a tunable valve seat. In general, the tunable check valve assemblies/tunable radial arrays of tunable suction and discharge valves will typically be tuned to different assembly resonant frequencies because of their different positions in a subassembly housing  78  (and thus in a pump housing as described herein). Pump housing resonant frequencies that are measured proximate the tunable suction and discharge valves will differ in general, depending on the overall pump housing design. In each case they serve to guide the choices of the respective assembly resonant frequencies for the valves. 
     Note that the combination of major components labeled in  FIG. 6  as a pump fluid end subassembly  88  is so labeled (i.e., is labeled as a subassembly) because typical fluid end configurations comprise a plurality of such subassemblies combined in a single machined block. Thus, in such typical (multi-subassembly) pump fluid end designs, as well as in less-common single-subassembly pump fluid end configurations, the housing is simply termed a “pump housing” rather than the “subassembly housing  78 ” terminology of  FIG. 6 . 
     Further as schematically-illustrated and described herein for clarity, each pump fluid end subassembly  88  comprises only major components: a pumping chamber  74 , with its associated tunable suction valve  95 , tunable discharge valve  97 , and piston/plunger  93  in their respective bores  76 ,  72  and  70  of subassembly housing  78 . For greater clarity of description, common fluid end features well-known to those skilled in the art (such as access bores, plugs, seals, and miscellaneous fixtures) are not shown. Similarly, a common suction manifold through which incoming pumped fluid is distributed to each suction bore  76 , and a common discharge manifold for collecting and combining discharged pumped fluid from each discharge bore  72 , are also well-known to those skilled in the art and thus are not shown. 
     Note that the desired check-valve function of tunable check valves  95  and  97  schematically-illustrated in  FIG. 6  requires interaction of the respective tunable check valve assemblies (see, e.g.,  FIGS. 1-5 ) with a corresponding (schematically-illustrated) tunable valve seat (see, e.g.,  FIGS. 7 ,  8 ,  10  and  11 ). The schematic illustrations of  FIG. 6  are only intended to convey general ideas of relationships and functions of the major components of a pump fluid end subassembly. Structural details of the tunable check valve assemblies that are in turn part of tunable check valves  95  and  97  of the invention (including their respective tunable valve seats) are illustrated in greater detail in other figures as noted above. Such structural details facilitate a plurality of complementary functions that are best understood through reference to  FIGS. 1-5  and  7 - 11 . 
     The above complementary functions of tunable check valves include, but are not limited to, closing energy conversion to heat via structural compliance, energy redistribution through rejection of heat to the pumped fluid and pump housing, vibration damping and/or selective vibration spectrum narrowing through changes in tunable check valve assembly compliance, vibration frequency down-shifting (via decrease in rebound characteristic frequency) through increase of rebound cycle time, and selective vibration attenuation through energy dissipation (i.e., via redistribution) at predetermined assembly resonant frequencies. 
       FIG. 7  is a schematic illustration of two views of an exploded partially-sectioned 3-dimensional view including a check valve body  10  and its convex valve seat interface  22 , together with concave mating surface  24  of tunable valve seat  20 . Mating surface  24  is longitudinally spaced apart from a pump housing interface surface  21 . A curved longitudinal section edge  28  of the tunable valve seat&#39;s mating surface  24 , together with a correspondingly greater curved longitudinal section edge  26  of the valve body&#39;s valve seat interface  22 , are shown schematically in detail view A to aid description herein of a rolling valve seal. 
     The correspondingly greater curvature of valve seat interface  22 , as compared to the curvature of mating surface  24 , effectively provides a rolling seal against fluid leakage which reduces wear on the surfaces in contact. The rolling seal also increases longitudinal compliance of a tunable suction or discharge valve of the invention, with the added benefit of increasing the rise and fall times of the closing energy impulse (thus narrowing the associated vibration spectrum). Widening the closing energy impulse increases rebound cycle time and correspondingly decreases rebound characteristic frequency. 
     Further regarding the terms “correspondingly greater curvature” or “correspondingly less curvature” as used herein, note that the curvatures of the schematically illustrated longitudinal section edges (i.e.,  26  and  28 ) and the surfaces of which they are a part (i.e., valve seat interface  22  and mating surface  24  respectively) are chosen so that the degree of longitudinal curvature of valve seat interface  22  (including edge  26 ) exceeds that of (i.e., has correspondingly greater curvature than) mating surface  24  (including edge  28 ) at any point of rolling contact. In other words, mating surface  24  (including edge  28 ) has correspondingly less curvature than valve seat interface  22  (including edge  26 ). Hence, rolling contact between valve seat interface  22  and mating surface  24  is always along a substantially circular line, the plane of which is transverse to the (substantially coaxial) longitudinal axes of valve body  10  and tunable valve seat  20 . 
     Note that although valve seat interface  22  and mating surface  24  (and other valve seat interface/mating surface combinations described herein) are schematically illustrated as curved, either may be frusto-conical (at least in part) in certain tuned component embodiments. Such frusto-conical embodiments may have lower fabrication costs and may exhibit suboptimal down-shifting performance and/or wear characteristics. They may be employed in relatively lower-pressure applications where other tunable component characteristics provide sufficient operational advantages in vibration control. 
     The above discussion of rolling contact applies to the alternate tunable valve seat  20 ′ of  FIG. 8 , as it does to the tunable valve seat  20  of  FIG. 7 .  FIG. 8  schematically illustrates a 3-dimensional exploded and partially-sectioned view of a tunable valve seat showing a mating surface (analogous to mating surface  24  of  FIG. 7 ) longitudinally spaced apart from a lateral support mounting surface  21 ′. But the lateral support mounting surface  21 ′ in  FIG. 8  differs from pump housing interface surface  21  of  FIG. 7  in that it facilitates adjustably securing a lateral support assembly  130  to alternate tunable valve seat  20 ′. Lateral support assembly  130  comprises first and second securable end spacers ( 110  and  124  respectively) in combination with a plurality of circular viscoelastic support elements ( 114 ,  118  and  122 ), each support element comprising a support circumferential tubular area (see areas  112 ,  116  and  120  respectively). Shear-thickening material in each support circumferential tubular area  112 ,  116  and  120  is chosen so each lateral support assembly  130  has at least one predetermined resonant frequency. Lateral support assemblies thus configured may be part of each tunable valve seat and each tunable plunger seal. When part of a tunable plunger seal, one or more lateral support assemblies  130  reside in at least one recess analogous to the packing box schematically illustrated adjacent to piston/plunger  93  (i.e., as a portion of piston/plunger bore  70 ) in  FIG. 6 . 
     Note also that in general, a tunable (suction or discharge) check valve of the invention may comprise a combination of a tunable check valve assembly  99  (see, e.g.,  FIG. 1 ) and a tunable valve seat  20  (see, e.g.,  FIG. 7 ) or a tunable valve seat  20 ′ (see, e.g.,  FIG. 8 ). Referring more specifically to  FIG. 6 , tunable suction check valve  95  is distinguished from tunable discharge check valve  97  by one or more factors, including each measured resonant frequency to which each tunable check valve is tuned so as to optimize the overall effectiveness of valve-generated vibration attenuation in the associated pump housing  78 . 
       FIGS. 9-11  show schematic exploded views of a nonlinear spring-mass damper  227 / 228 / 229 / 230 , which may be incorporated in a tunable check valve assembly embodiment  210 .  FIGS. 9-11  can each be understood as schematically illustrating a tunable check valve assembly with or without a peripheral groove viscoelastic element. That is, each figure may also be understood to additionally comprise a viscoelastic groove element analogous to groove element  54  (see  FIG. 2 ) residing in groove  218 ′/ 218 ″ (see FIG.  9 )—this groove element is not shown in exploded  FIGS. 9-11  for clarity, but may be considered to comprise at least one circumferential tubular area analogous to tubular area  58  in groove element  54  (see  FIG. 2 ), each tubular area  58  being substantially filled with at least one shear-thickening material  80  chosen to achieve at least one predetermined assembly resonant frequency. 
     Referring to  FIG. 9 , Belleville springs  227 / 228 / 229  are nonlinear, and they couple mass  230  to the valve body base plate  216  and the proximal valve body portion  214 . Additionally, dilatant liquid  242  is optionally added (via sealable ports  222  and/or  220 ) to central internal cavity  224  to immerse nonlinear spring-mass damper  227 / 228 / 229 / 230 . The nonlinear behavior of dilatant liquid  242  in shear (as, e.g., between Belleville springs  227  and  228 ) expands the range of tuning the nonlinear spring-mass damper  227 / 228 / 229 / 230  to a larger plurality of predetermined frequencies to reduce “ringing” of valve body  214 / 216  in response to a closing energy impulse. 
     To clarify the function of nonlinear spring-mass damper  227 / 228 / 229 / 230 , mass  230  is shown perforated centrally to form a washer shape and thus provide a passage for flow of dilatant liquid  242  during longitudinal movement of mass  230 . This passage is analogous to that provided by each of the Belleville springs  227 / 228 / 229  by reason of their washer-like shape. 
       FIG. 10  shows an exploded view of an alternate embodiment of a tunable check valve comprising the tunable check valve assembly  210  of  FIG. 9 , plus a tunable valve seat  250 .  FIGS. 10 and 11  schematically illustrate two views of an exploded partially-sectioned 3-dimensional view including a valve body  214 / 216  and its valve seat interface  234 , together with mating surface  254  of tunable valve seats  250  and  250 ′. Mating surface  254  is longitudinally spaced apart from pump housing interface surface  252  in  FIG. 10 , and from lateral support mounting surface  252 ′ in  FIG. 11 . In  FIG. 10 , a curved longitudinal section edge  256  of the tunable valve seat&#39;s mating surface  254 , together with a correspondingly greater curved longitudinal section edge  236  of valve seat interface  234 , are shown schematically to aid description herein of a rolling valve seal. 
     Note that valve body  214 / 216  may be fabricated by several methods, including that schematically illustrated in  FIGS. 9-11 . For example, circular boss  215  on proximal valve body portion  214  may be inertia welded or otherwise joined to circular groove  217  on valve body base plate  216 . Such joining results in the creation of peripheral seal-retention groove  218 ′/ 218 ″ having proximal groove wall  218 ′ and distal groove wall  218 ″. 
     To enhance scavenging of heat due to friction loss and/or hysteresis loss, liquid polymer(s)  242  may be augmented by adding nanoparticles which are generally invisible to the eye as they are typically dispersed in a colloidal suspension. Nanoparticles comprise, for example, carbon and/or metallic materials such as copper, beryllium, titanium, nickel, iron, alloys or blends thereof. The term nanoparticle may conveniently be defined as including particles having an average size of up to about 2000 nm. See, e.g., the &#39;320 patent. 
     The correspondingly greater curvature of valve seat interface  234 , as compared to the curvature of mating surface  254 , effectively provides a rolling seal against fluid leakage which reduces wear on the surfaces in contact. The rolling seal also increases longitudinal compliance of a tunable suction or discharge valve of the invention, with the added benefit of increasing the rise and fall times of the closing energy impulse (thus narrowing the associated vibration spectrum). 
     Further regarding the term “correspondingly greater curvature” as used herein, note that the curvatures of the schematically illustrated longitudinal section edges (i.e.,  236  and  256 ) and the surfaces of which they are a part (i.e., valve seat interface  234  and mating surface  254  respectively) are chosen so that the degree of longitudinal curvature of valve seat interface  234  (including edge  236 ) exceeds that of (i.e., has correspondingly greater curvature than) mating surface  254  (including edge  256 ) at any point of rolling contact. Hence, rolling contact between valve seat interface  234  and mating surface  254  is always along a substantially circular line, the plane of which is transverse to the (substantially coaxial) longitudinal axes of valve body  214 / 216  and tunable valve seat  250 . (See notes above re frusto-conical valve seat interface shapes and mating surfaces). 
     The above discussion of rolling contact applies to the alternate tunable valve seat  250 ′ of  FIG. 11 , as it does to the tunable valve seat  250  of  FIG. 10 . But the lateral support mounting surface  252 ′ in tunable check valve  399  of  FIG. 11  differs from pump housing interface surface  252  of  FIG. 10  in that it facilitates adjustably securing a lateral support assembly  330  to alternate tunable valve seat  250 ′ to form tunable valve seat  389 . Lateral support assembly  330  comprises first and second securable end spacers ( 310  and  324  respectively) in combination with a plurality of circular viscoelastic support elements ( 314 ,  318  and  322 ), each support element comprising a support circumferential tubular area ( 312 ,  316  and  320  respectively). 
     Note that in general, a tunable (suction or discharge) check valve of the invention may comprise a combination of a tunable check valve assembly  210  (see, e.g.,  FIG. 9 ) and a tunable valve seat  250  (see, e.g.,  FIG. 10 ) or a tunable valve seat  250 ′ (see, e.g.,  FIG. 11 ). Referring more specifically to  FIG. 6 , tunable suction valve  95  is distinguished from tunable discharge check valve  97  by one or more factors, including each measured or estimated resonant frequency to which each tunable check valve is tuned so as to optimize the overall effectiveness of valve-generated vibration attenuation in the associated pump housing  78 .