Abstract:
The inventive passive damping system features the unique harmonization of: (i) a constrained-layer damping subsystem (wherein an elastomer serves as constrained damping material); (ii) an entrained damping subsystem (wherein a particulate serves as entrained damping material); and, (iii) a tuned damping subsystem (wherein modal properties of certain inventive components have been selectively varied in accordance with anticipated resonance frequencies). The invention&#39;s effectiveness is aggregative; the total loss factor for the inventive damping system equals the sum of the individual loss factors for the damping subsystems. Consequently, the invention affords a high loss factor in a broad frequency range. Especially in applications involving control of extremely high vibrations, the inventive damping methodology is more efficient and economical than are common damping methodologies.

Description:
STATEMENT OF GOVERNMENT INTEREST 
     The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to damping, more particularly to methods, apparatuses and systems for passively effectuating damping for controlling vibrations. 
     Vibrations are often unwanted because they can cause structural weakening, metal fatigue, bothersome noise, etc. Particularly undesirable are many situations wherein a power-driven source (e.g., a motor) produces a frequency at which an attached structure naturally vibrates, an occurrence known as “resonance.” 
     Various types of passive damping treatments have been known to be effective in reducing the amplitude of vibrations at resonant frequencies. The known effective passive damping methodologies include “conventional” damping, “entrained” damping and “tuned” damping. 
     Two known kinds of conventional damping treatment are unconstrained (unconstrained-layer) damping treatment and constrained-layer damping treatment. All of these known passive damping mechanisms, though often highly (or at least moderately) effective for particular applications, nonetheless have limited capabilities in terms of damping performance. 
     Tuned damping, for example, produces a relatively large loss factor in a narrow frequency band. Therefore, tuned damping is generally applied to reduce single mode vibration. In contrast, constrained-layer damping is effective in a broad frequency, but its loss factor is relatively small. Because of this, constrained-layer damping treatment is relatively effective for controlling the vibrations in higher frequencies, but is less effective in lower frequencies. 
     A greater amount of damping loss factor has been known to be achieved by applying an increased number of similar passive damping treatments on the structure; however, this sort of “pluralizing” approach to individual units yields a diminishing return in damping effectiveness as the amount of damping treatment (i.e., the number of units) increases. 
     Active (as distinguished from passive) vibration control methodologies have also been known to effectively reduce vibrations. However, due to limitations regarding processor speed and actuator power delivery, active vibration control has proven rather impractical in high frequency and multi-mode vibration control. Moreover, the costs associated with installation and maintenance of active vibration control systems, vis-a-vis&#39; passive vibration control systems, are comparatively high. 
     Generally speaking, depending upon the application, a damping treatment is considered to be effective if the vibrational reduction caused by the damping treatment in turn results in a decrease in at least one of the following: sound radiation; structural stresses attendant fatigue problems in structural members; and, structural-borne wave propagations (i.e., the transmission of vibrational energy along the structure). 
     SUMMARY OF THE INVENTION 
     In view of the foregoing, it is a principal object of the present invention to provide a passive vibration damping methodology which is effective over a broad range of frequencies. 
     It is a further object of the present invention to provide such a methodology which is economical. 
     The passive vibration damping device according to this invention is conveniently identified herein by the acronym “TBVD” for “Tuned Broadband Vibrational Dissipator.” The inventive TBVD provides large loss factors in a broad frequency band. In typical inventive practice, the inventive TBVD is implemented as an add-on damping device. 
     In accordance with many embodiments of the present invention, the inventive TBVD is a device for effectuating passive vibration damping of a structure which is subject to excitation by a source. The inventive device comprises a viscoelastic layer, a hollow member and granular material. The viscoelastic layer adjoins the hollow member. The granular material at least partially fills the hollow member. 
     According to many inventive embodiments, the present invention provides a method for effectuating passive vibration damping of a structure which is subject to excitation by a source. The inventive method comprises: providing a hollow member; at least partially filling the hollow member with granular material; and, affixing a viscoelastic layer to the hollow member. 
     The present invention features a structural integration which affords multi-damping simultaneity. Inventively integrated are various structural components which, customarily, are separately utilized in furtherance of individually corresponding passive damping mechanisms. This inventive structural integration effectuates the synchronization of three passive damping mechanisms—viz., constrained-layer damping, entrained damping and tuned damping. The present invention thereby propitiously affords a cumulative damping effect which is the aggregation of the individual damping effects corresponding to the respective damping mechanisms. 
     Thus the present invention, unlike previous damping treatments, is designed to simultaneously operate a diverse plurality of damping mechanisms so as to produce a large loss factor in a broad frequency band. Moreover, the present invention provides multiple tuning capability which can be tailored to suppress multiple resonant modes of the structure. Hence, the inventive damping treatment provides a cost-effective way of controlling critical vibrations. 
     The present invention is especially advantageous insofar as controlling extremely large vibrations. The customary approach to control of very great vibrations involves application of a large amount of conventional damping treatment (which implements elastomeric material)—an approach necessitated by the relatively small loss factor associated with conventional damping treatment. In particular, this invention cost-effectively reduces excesively large flexural vibrations in beam-like, plate-like and cylindrical structures subjected to various loading conditions in a broad frequency range. 
     Depending on the application, inventive practice can succeed in any or all of the following: (i) reducing the radiated acoustic noise from one or more structures; (ii) reducing the structural-borne transmission path or paths; (iii) providing a comfortable and quiet environment for a ship or a building; (iv) reducing the requirements for vibration-sensitive equipment. 
    
    
     Other objects, advantages and features of this invention will become apparent from the following detailed description of the invention when considered in conjunction with the accompanying drawings. 
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In order that the present invention may be clearly understood, it will now be described by way of example, with reference to the accompanying drawings, wherein like numbers indicate the same or similar components, and wherein: 
     FIG.  1 ( a ) is a diagrammatic cross-sectional representation of constrained-layer damping treatment, illustrating the deformed structural response of this damping mechanism. 
     FIG.  1 ( b ) is a diagrammatic cross-sectional representation of entrained damping treatment, illustrating the deformed structural response of this damping mechanism. 
     FIG.  1 ( c ) is a diagrammatic cross-sectional representation of tuned damping treatment, illustrating the deformed structural response of this damping mechanism. 
     FIG. 2 is a graphical representation which typifies loss factor as a function of frequency for each of the various damping treatments shown in FIG.  1 ( a ), FIG.  1 ( b ), FIG.  1 ( c ) and FIG.  3 . 
     FIG. 3 is a diagrammatic cross-sectional representation of a preferred embodiment of an inventive TBVD. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     According to conventional passive damping treatment, energy is dissipated in a layer of viscoelastic damping material which is attached to the structure. When the structure deforms, strains develop in the viscoelastic damping material, irreversible relaxation occurs, and strain energy is converted to heat. The key to effective conventional damping treatment, therefore, is to maximize the strain energy in the viscoelastic layer. Conventional damping treatment is commonly applied in either of two ways, viz., unconstrained (unconstrained-layer) damping treatment and constrained-layer damping treatment. 
     According to conventional unconstrained damping treatment, the viscoelastic material is attached to the structure. Energy dissipation is caused by the extensional strains in the viscoelastic layer. 
     Reference is now made to FIG.  1 ( a ), wherein is shown the deformed structural response of conventional constrained-layer damping treatment. According to constrained-layer damping treatment, a viscoelastic layer  10  is sandwiched between a base layer structure  12  and a relatively stiff constraining layer  14 . Constraining layer  14  causes shear strains to develop in viscoelastic layer  10  when base layer structure  12  bends, because constraining layer  14  is less extensive than base layer structure  12 . Viscoelastic layer  10 , intermediate base layer structure  12  and constraining layer  14 , thus acts as the constrained layer of the constrained-layer damping system. 
     With reference to FIG. 2, the loss factor achievable by constrained-layer damping, described by curve c, exhibits mild frequency dependence and generally is larger than that obtained by unconstrained-layer treatments. As shown in FIG. 2, the loss factor for the constrained-layer damping is rather broad in effect. 
     The effectiveness of the constrained-layer damping treatment depends on a number of variables. The important properties of the constraining layer include its thickness, its modulus of elasticity, and its density. The important properties of the viscoelastic material used in the constrained-layer damping treatment include its thickness, its density, its modulus of elasticity, and its damping loss factor. The latter two properties (modulus of elasticity; damping loss factor) of the viscoelastic material are functions of both temperature and frequency. 
     Referring to FIG.  1 ( b ), according to entrained damping treatment, a hollow structure  16  (e.g., a tube, tubular beam or other hollow structural object) is filled with granular material  18  such as sand or beads. Like conventional damping treatment, the key to entrained damping treatment performance is to deliver strain energy to the damping material, where it can be dissipated by relaxation mechanisms. Unlike conventional damping treatment, the damping material is granular filler material  18  rather than viscoelastic layer  10 . Inter-particle friction of granular material  18  may also dissipate energy, but its importance has not been quantified. 
     The lowest frequency where entrained damping performance is high is the so-called “cut-on” frequency. The cut-on frequency is the fundamental cross-sectional resonance frequency of granular filler material  18  and also is the lowest frequency at which waves can propagate in granular filler material  18 . At and above cut-on, a structure transmits energy into the granular filler material  18  in the form of waves. Below cut-on, granular filler material  18  essentially moves with the structure as a rigid body, adding mass to the structure. 
     Still referring to FIG.  1 ( 1   b ) and FIG. 2, energy dissipation is large at the cross-sectional resonance of granular filler material  18 , due to vigorous filler motion. Loss factor peaks for entrained damping occur as described by curve e in FIG.  2 . The largest peak loss factor occurs at the lowest cross-sectional resonance frequency of granular filler material  18 . The cross-sectional resonance frequencies depend on the wave speed of granular filler material  18  and the size of the cross-section. This property gives an opportunity to tune (or design) the entrained damping mechanisms. 
     Reference now being made to FIG.  1 ( c ), a viscoelastic compliance layer  20  is sandwiched between a base layer structure  22  and a relatively thick elastic constraining layer  24 . The tuned damper utilizes a viscoelastic compliance layer  20  and an elastic constraining layer  24  which are each sized to concentrate both reactive and dissipative vibration control mechanisms over a preselected frequency band. 
     There are two methods of “tuning” the damper (thereby selectively damping the vibrations of the structure) in accordance with tuned damping treatment. According to the first method, elastic constraining layer  24  can act as a lumped tuning mass; tuning is achieved by compressing viscoelastic compliance layer  20 . According to the second method, the combination of elastic constraining layer  24  and viscoelastic compliance layer  20  is designed to have one of its eigen frequencies coincide with the frequency of interest; tuning is achieved by adjusting this frequency. 
     At the design frequency, the tuned damper can be constructed to act as a concerted group of transverse-compressional damping mechanisms which take advantage of the out-of-phase motion between viscoelastic compliance layer  20  and elastic constraining layer  24 , thereby producing relatively high composite loss factors in a relatively narrow spectral band, as described by curve t in FIG.  2 . 
     Generally, the response of a structure will differ at each of its different “natural frequencies.” The structure will exhibit a different deformation pattern (“mode shape”), depending on which resonant (natural) frequency the excitation is coincident with. People who are skilled in the art of “modal analysis” evaluate the natural characteristics of structures in terms of their natural frequencies and mode shapes. The natural frequency (natural frequencies) of a structure is (are) determined by the mass distribution and the stiffness distribution in the structure. 
     Below and above the design frequency, the tuned damper (such as shown in FIG.  1 ( c )) can control radiation from a structure (such as base layer structure  22 ) by altering the structure&#39;s modal character (e.g., by increasing mass per unit area and modal stiffness). In other words, the modal character of the structure can be altered so as to subdue a vibrational mode which is significantly resonant due to excitation of the structure by an excitation source. The structure&#39;s modal character can be adjusted by increasing (or decreasing) its mass per unit area and/or its modal stiffness. 
     Reference now being made to FIG. 3, the inventive TBVD is an adjunct (accessory) passive damping treatment device which is designed to concurrently operate the three potentially highly effective damping mechanisms shown in FIG.  1 ( a ), FIG.  1 ( b ) and FIG.  1 ( c )—viz., constrained-layer damping, entrained damping and tuned damping, respectively. 
     The inventive TBVD comprises viscoelastic layer  26 , hollow member  28  and granular filler material  30  (e.g., beads or sand or other particulate). According to this invention, hollow member  28  is a hollow structural body, such as a hollow rectangular metal (e.g., steel) box, which typically has a surface congruous with a surface of the subject structure (such as base plate  32  shown in FIG.  3 ). Granular filler material  30  (beads are shown in FIG. 3) at least partially fills hollow member  28 . For many inventive embodiments, it is preferable that granular filler material  30  completely fills or substantially fills hollow member  28 . 
     Granular filler material  30  can comprise any aggregation of discrete bodies which lends itself to being selectively changed with respect to its overall mass stiffness and loss factor. In the light of this disclosure, it is apparent to the ordinarily skilled artisan that granular filler material  30  can be designed in a variety of ways in furtherance of optimizing the tuning frequency and increasing the loss factor. Accordingly, granular filler material  30  can be, depending upon the inventive embodiment, either homogeneous or heterogeneous in size, shape and/or material composition. 
     For instance, some inventive embodiments can effectively implement composite bead-like granular filler material, wherein each composite sphere comprises a metal (e.g., steel) core and a high loss viscoelastic material covering. For typical such inventive embodiments, the loss factor of the viscoelastic covering is in the range between about 0.1 and about 0.5. Such material combination of each discrete spherical body would beneficially afford high mass as well as high loss factor. These composite balls comprising viscoelastic-coated metal (e.g., steel) can constitute all of granular filler material  30 , or can be combined with one or more other kinds of granular filler material  30 . In fact, depending upon the inventive embodiment, the composite balls themselves can be either homogeneous or heterogeneous in size, shape and/or material composition. 
     The inventive TBVD is attached onto a structural foundation (for example, a base layer structure such as base plate  32 ) by means of a self-adhesive viscoelastic layer  26 . Viscoelastic layer  26  is sandwiched between base plate  32  and hollow member  28 . More specifically, viscoelastic layer  26  is sandwiched between base plate  32  and member face  34 . 
     In the light of this disclosure, it is understood by the ordinarily skilled artisan that inventive practice can render attachment of the inventive TBVD (e.g., via self-adhesive viscoelastic layer  26 ) to any structural foundation, assuming the suitability of such attachment for furthering inventive purposes. The structural foundation itself is typically the entity for which effectuation of inventive damping is exclusively or principally intended. Generally, the inventive TBVD is directly attached to the structural foundation—that is, the subject structure itself to which inventive damping is being applied. 
     The subject structure can be a stand-alone body or can be an interposed body between another structural entity and the inventive TBVD. Whether the subject structure is disconnected or connected to another structural entity, the inventive TBVD essentially effects inventive damping of the subject structure. 
     For many inventive applications, the subject structure is approximately shaped like a plate (as shown in FIG.  3 ), a beam or a cylinder. It is readily apparent to the ordinarily skilled artisan who reads this disclosure that the inventive principles illustrated in FIG. 3 are readily applicable to subject structures having a variety of shapes. Typically, the inventive apparatus engages a substantially smooth surface, either flat or curved, of the subject structure. 
     It is readily envisioned, for instance, that base plate  32  is, instead, a base beam  32 , so that hollow member  28  would similarly have a flat member side  34  in conformity with the flatness of base beam  32 . As another example, it is readily envisioned that base plate  32  is, instead, a base cylinder  32 , so that hollow member  28  would have a curved member side  34  (eg., slightly curved) in conformity with the curvature of base cylinder  32 . 
     Member face  34  is a solid, planar, containment layer (the upper horizontal layer, as shown in FIG. 3) which forms a part of hollow member  28  (which contains granular filler material  30 ). Member face  34  represents a geometric side of the geometric shape of hollow member  28 . 
     Many inventive embodiments provide two opposite member faces as part of hollow member  28 . As shown in FIG. 3, member face  35  is opposite member face  34 . Member face  35  similarly is a solid, planar, containment layer (the lower horizontal layer, as shown in FIG. 3) which forms a part of hollow member  28 . Member face  34  similarly represents a geometric side of the geometric shape of hollow member  28 . 
     For many inventive embodiments, hollow member  28  is trapezoidal in cross-section; that is, the two opposite member faces  34  and  35  are approximately planar and approximately parallel. For instance, such a hollow member  28  can be rectangular in cross-section (eg., box-shaped or disk-shaped), such as shown in FIG.  3 . Thus, one may consider hollow member  28  shown in FIG. 3 to be a hollow rectangular metal (e.g., steel) box, wherein member faces  34  and  35  are approximately equivalent, each being a flat, rectangular, plate-like, steel section of hollow member  28 . 
     It is readily envisioned, for instance, that base plate  32  is, instead, a base beam  32 , so that hollow member  28  would similarly have an approximately rectangular cross-section wherein approximately parallel, opposite member sides  34  and  35  are each flat in conformity with the flatness of base beam  32 . As another example, it is readily envisioned that base plate  32  is, instead, a cylinder  32 , so that hollow member  28  would have an approximately rectangular cross-section wherein approximately parallel, opposite member sides  34  and  35  equivalently are curved (e.g., slightly curved) in conformity with the curvature of base cylinder  32 . 
     Viscoelastic layer  26  and member face  34  act, together with a foundational constraint upon the opposite side of viscoelastic layer  26 , toward achieving the constrained-layer damping aspect of the inventive TBVD. As shown in FIG. 3, base plate  32  serves as the foundational constraint. Viscoelastic layer  26  is sandwiched, and thereby constrainable, between structural face  34  and base plate  32 . 
     Member face  34  thus functions as the inventive TBVD&#39;s constraining layer for viscoelastic layer  26 , wherein viscoelastic layer  26  is being oppositely constrained by base plate  32 . Viscoelastic layer  26  is situated intermediate base layer  32  and member face  34 , each of which exerts a constraining influence of viscoelastic layer  26 . Viscoelastic layer  26  operates as the constrained layer within the invention&#39;s constrained-layer damping subsystem. 
     Granular filler material  30  (e.g., beads, as shown in FIG.  3 ), which completely or partially fills hollow member  28 , represents the entrained damping aspect of the inventive TBVD. According to the invention&#39;s entrained damping subsystem, granular filler material  30  behaves as the particulate damping material which is entrained within hollow member  28 . 
     The combination of viscoelastic layer  26 , hollow member  28  and granular filler material  30  performs the inventive tuned damping. Each of these constituents of the invention&#39;s tuned damping subsystem is alterable in furtherance of attaining a desired modal character of the inventive TBVD, and hence a desired modal character of the structure which the inventive TBVD engages. 
     According to the tuned damping aspect of the present invention, any one, any two or all three of the following parameters—(i) the stiffness of viscoelastic layer  26 , (ii) the mass of hollow member  28 , and/or (iii) the mass of granular filler material  30 —can be “tuned” (i.e., selectively changed) in order to suppress a dominant resonant mode of base plate  32 . Generally in inventive practice, the inventive “tuning” objective remains to adjust the modal character of the inventive TBVD (and hence, of the structure) in accordance with the driving frequency or frequencies of the excitation source. 
     In typical inventive practice, the stiffness of viscoelastic layer  26  can be varied by varying viscoelastic layer  26 , and/or by varying the degree to which viscoelastic layer  26  is compressed between structural face  34  and base plate  32 . The mass of hollow member  28  can be varied by varying hollow member  28 , and/or by adding structural mass thereto or subtracting structural mass therefrom. Similarly, the mass of granular filler material  30  can be varied by varying granular filler material  30 , and/or by adding granular filler material  30  to, or subtracting granular filler material  30  from, the space within hollow member  28 . 
     It is understood by the ordinarily skilled artisan who reads this disclosure that viscoelastic layer  26  is inventively tailored to suit a particular embodiment or application, and thus can be characterized by any degree of stiffness or by any loss factor, depending on such embodiment or application. 
     Variation of mass of hollow member  28  can be inventively achieved, for instance, by providing one or more removably attachable weighted objects which to some extent or in some respect conform with the shape of hollow member  28 . For example, supplemental metal plate(s) can be attached to or detached from member face  34  or member face  35 . Alternatively, supplemental metal rectangles or rings can be attached to or detached from lateral member periphery  37 . 
     In the light of this disclosure, various techniques for adjusting or altering physical or material characteristics of the inventive TBVD in furtherance of inventive modal tuning will be apparent to the ordinarily skilled artisan. For instance, accessibility to/from the interior cavity of hollow member  28  can be provided by an inlet/outlet valve or a door. Main components of the inventive TBVD can be modularized. Hollow member  28  can be so constructed as to permit ease of assembly and disassembly, and/or ease of annexation and removal of supplemental parts. Viscoelastic layers  26  having appropriate dimension and varying properties can be made available and used interchangeably. 
     The effective loss factor of the TBVD, η TBVD  is the sum of all the loss factors produced by individual damping mechanisms acting on the system. That is, 
     
       
         η TBVD =η t +η e +η c , 
       
     
     where η t , η e  and η c  are the loss factors for tuned damping, entrained damping and constrained-layer damping, respectively. 
     The expected loss factor for the inventive TBVD is described by curve TBVD in FIG.  2 . Due to the multi-damping mechanisms acting simultaneously on base plate  32 , the inventive damping treatment produces an unusually large loss factor in a broad frequency band. This inventive benefit is particularly attractive in controlling excessively large vibrations. Normally, extremely great vibrations require a large amount of conventional damping treatment, since the damping loss factor associated with conventional damping treatment is relatively small. 
     Other embodiments of this invention will be apparent to those skilled in the art from a consideration of this specification or practice of the invention disclosed herein. Various omissions, modifications and changes to the principles described may be made by one skilled in the art without departing from the true scope and spirit of the invention which is indicated by the following claims.