High stiffness vibration damping apparatus, methods and systems

Vibration damping apparatus, systems, objects including such apparatus and systems, and vibration damping methods. The vibration damping involves amplifying a vibration-induced displacement and damping the amplified displacement.

BACKGROUND

The present inventions relate generally to vibration damping.

2. Related Art

Vibration damping materials are employed in a wide variety of mechanical systems to damp vibrations that can degrade performance of the systems. The present inventors have determined conventional vibration damping materials are susceptible to improvement. For example, low stiffness materials are commonly used for vibration damping because their flexible lattices are inherently better at dissipating energy. In some instances, however, devices must be securely held in place despite the fact that the devices are sensitive to, or are the source of, vibrations. Launch vehicle adaptors, motor mounts, and high precision moving devices are examples of such devices. Low stiffness materials are less than optimal here because they permit movement, as are conventional high stiffness materials because they have relatively poor damping characteristics.

SUMMARY

A vibration damping apparatus in accordance with one embodiment of a present invention includes a displacement conversion device configured to convert displacement in a first direction into displacement in a second direction, a motion amplifier responsive to displacement in the second direction, and a motion damper operably connected to the motion amplifier. The present inventions also include systems and objects with such vibration damping apparatus.

A vibration damping method in accordance with one embodiment of a present invention includes the steps of converting a vibration-induced displacement in a first direction into a displacement in a second direction, amplifying the displacement in the second direction to create an amplified displacement, and damping the amplified displacement.

There are a variety of advantages associated with such a vibration damping apparatus, systems, objects and methods. For example, the present vibration damping apparatus may be configured such that it is relatively stiff in the direction of the vibration forces (e.g., the first direction), while providing better damping characteristics than have been heretofore associated with materials and structures having the same stiffness in the direction of the vibration forces.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

The following is a detailed description of the best presently known modes of carrying out the inventions. This description is not to be taken in a limiting sense, but is made merely for the purpose of illustrating the general principles of the inventions.

A vibration damping apparatus (or “damping apparatus”) in accordance with one embodiment of a present invention is generally represented by reference numeral100inFIGS. 1 and 2. The exemplary damping apparatus100includes a displacement conversion device102, a motion amplifier (or “displacement amplifier”)104, and a motion damper (or “displacement damper”)106, each of which is discussed in greater detail below. Briefly, the displacement conversion device102converts displacement thereof along a first axis A1(or “in a first direction”) caused by vibrational force FVIBinto displacement along a second axis A2(or “in a second direction”). The first and second axes A1and A2(or “different directions”) may be transverse (including perpendicular as shown) or otherwise non-coaxial. The period of the back and forth vibration-induced displacement along each axis is the same. In at least some instances, the magnitude of the displacement along the second axis A2(i.e., the displacement distance Δ2) is greater than the magnitude of the displacement along the first axis A1(i.e., the displacement distance Δ1) and, in view of the fact that the periods are the same, the velocity of the displacement along the second axis is greater than the velocity of the displacement along the first axis.

The motion amplifier104includes an interface member108that also moves along the second axis A2and whose motion is damped by the motion damper106. The displacement of the interface member108along the second axis A2is, relative to the displacement of the displacement conversion device along the first axis A1, amplified both in magnitude and velocity. In particular, the motion amplifier104creates displacement (i.e., the displacement distance Δ3) at the interface member108that is greater than the displacement distance Δ2in response to the displacement of portions of the displacement conversion device102along the second axis A2. The period of the back and forth vibration-induced displacement of the interface member108is the same as that of the displacement conversion device102along axes A1and A2. As such, the velocity of the interface member108is greater than the velocity of the displacement conversion device102along axis A1and along axis A2. Thus, in the illustrated implementation, the vibration-induced displacement (and velocity) that occurs along axis A1is amplified, and then the amplified displacement (and velocity) is itself amplified.

Given that damping force is equal to the damping coefficient multiplied by the velocity to the damped object (Fd=cv), damping the twice amplified motion at the interface member108results in far more effective damping of vibrations applied to damping apparatus100than would be the case if the motion damper106was acting directly on movement of the displacement conversion device102along the first axis A1or the second axis A2. As such, the present vibration damping apparatus100may be configured such that it effectively damps vibrations despite being relatively stiff in the direction of the vibration forces.

The exemplary motion amplifier104includes a positive spring110(i.e., a spring with a positive spring constant K1) and a negative spring112(i.e., a spring with a negative spring constant K2). As used herein, a “negative spring” is spring which has a stress-strain (or load-displacement) curve with a negative slope. In some instances, the negative slope will be over only a portion of the stress-strain (or load-displacement) curve. Here, the spring may be selected, preloaded and/or physically restrained such that it operates within the region of negative slope. As is explained below, the spring constants K1and K2are close to, but not exactly, equal and opposite in value. The absolute value (or “magnitude”) of the negative spring constant K2is slightly less than the absolute value (or “magnitude”) of the positive spring constant K1. As used herein, “slightly less” is 1% to 10% less.

By way of background, it should be noted that when positive and negative springs which have spring constants that are equal in absolute value, i.e., have equal and opposite spring constants, are combined in parallel the resulting spring constant is zero. Conversely, when two springs of equal and opposite spring constant are combined in series, the resulting spring constant is infinity. If an outside force is applied to the positive/negative spring series, the overall length of the spring series remains constant, but the interface between the positive and negative springs will move as the positive spring compresses and the negative spring expands in response to the force. The inventors herein have determined that this phenomenon is magnified when there is slight difference between the absolute values of the spring constants in the positive/negative spring series. The magnitude of the interface displacement is inversely proportional to the percent difference between the absolute values of the positive and negative spring constants. Put another way, motion amplification=K1/(IK1I−IK2I). If, for example, the percent difference between the spring constant absolute values is 2%, with a slightly positive overall spring constant, then the displacement at the interface will be 50 times the combined displacement at the ends of the positive/negative spring series. The present inventors have also determined that the positive/negative spring series, which is slightly positive in overall spring constant, is relatively unstable. As such, stabilization of a positive/negative spring series may be required.

Referring more specifically toFIG. 2, the configuration of the displacement conversion device102in the illustrated embodiment is such that it defines a spring constant K3(or “stiffness”) in the direction of the second axis A2and a spring constant K4(or “stiffness”) in the direction of the first axis A1. Spring constant K3is a positive spring constant that stabilizes the motion amplifier104that includes positive and negative springs110and112. Spring constant K4is a positive spring constant that defines the stiffness of the damping apparatus100in the direction of the vibrational force FVIB. Spring constant K3is greater than the effective spring constant of the positive/negative spring series KEFF, where KEFF=(K1K2)(/K1+K2). For example, KEFFmay range from 0.5 K3to 0.9 K3. Spring constant K4, on the other hand, should be high enough, given the expected magnitude of the vibrational force FVIBassociated with the intended application, that the displacement along the first axis A1(i.e., the displacement distance Δ1) is minimized, but not so high that the displacement is non-existent, as it is the displacement along the first axis A1that is amplified along axis A2for damping.

For any particular damping apparatus, there is an optimal value for the damping coefficient c of the motion damper106, i.e., a value that results in the most damping for that system.FIG. 2Ashows the force versus displacement curves for otherwise identical damping apparatuses with different damping coefficients, including the optimum damping coefficient c for that apparatus, damping coefficients that are less (0.1 c and 0.01 c) and damping coefficients greater (10 c and “infinite,” i.e., high enough that the interface member108does not move). The most damping occurs where the area within the associated hysteresis curve is the greatest.FIG. 2Aalso shows that damping apparatus in accordance with the present inventions can be configured (or “tuned”) for a particular application. Some applications may, for example, call for greater stiffness and this can be achieved by increasing the damping coefficient with the understanding that the damping will be less than optimal.

Turning toFIGS. 3 and 4, the exemplary damping apparatus200illustrated therein operates in the manner described above and includes structures that are functionally similar to those illustrated inFIGS. 1 and 2. To that end, the exemplary damping apparatus200includes a displacement conversion device202, a motion amplifier204with an interface208, and a motion damper206. The displacement conversion device202converts (and amplifies) displacement thereof along the first axis A1caused by vibrational force FVIBinto greater displacement (and velocity) along the second axis A2, the motion amplifier204further amplifies the already amplified displacement (and velocity) along the second axis A2, and the twice amplified motion is then damped by the motion damper206at the motion amplifier interface208.

The exemplary displacement conversion device202includes a pair of arcuate members214and216, with inner surfaces214aand216aand outer surfaces214band216b, which are secured to one another at their longitudinal ends. The arcuate members214and216function like leaf springs, and the length, width, thickness, arc and materials may be selected such that, when combined, the displacement conversion device202will have the desired spring constant K3(along axis A2) and spring constant K4(along axis A1). The arcuate members214and216may be formed from any material, or combination of materials (e.g., a multi-layer composite), that is appropriate for the intended application. Suitable materials include, but are not limited to, plastics, metals such as aluminum and steel, and composites such as fiber reinforced resin composites. The arcuate members214and216may also be identical (as shown) or may be different in one or more aspects such as, for example, their curvature, thickness or material.

In addition to the interface208, the exemplary motion amplifier204includes a positive spring210and a negative spring212. The exemplary springs210and212are positioned on the outer surfaces214band216bof the conversion device arcuate members214and216in the illustrated embodiment. The outer surfaces214band216bsupport the outer rims of the springs210and212and include indentations under the springs that allow the springs to compress. The interface208mounts the springs210and212to the arcuate members214and216and, to that end, includes a rod218and a pair of end caps220and222that are secured to the rod. The rod218extends through the springs210and212and the arcuate members214and216, and the end caps220and222engage the springs. So arranged, the illustrated interface208and springs210and212are connected in series. i.e., spring-interface-spring. The rod218is also movable relative to the arcuate members214and216. The connectors between the rod218and end caps220and222may be threaded connectors so that the distance between the end caps220and222can be adjusted to, for example, add and/or adjust a preload on the springs210and212. Such preloading is discussed below with reference toFIGS. 5-7. The interface208also includes a damper engagement device224, which may be a flat plate as it is in the illustrated embodiment, that is secured to (and therefore moves with) the rod218.

Turning to the motion damper206, a wide variety of dampers may be employed. Such dampers may include, but are not limited to, sheets of high damping materials such as rubber, silicone, and foams (e.g., closed cell foams), frictional dampers, and mechanical apparatus such as shock absorbers and other hydraulic and pneumatic dampers. In the illustrated implementation, and although the present inventions are not so limited, the motion damper206includes a plurality of hollow hourglass-shaped machines226which are filled with regions of incompressible fluid that are separated from one another by a compressible material or gas bubble. Briefly, and referring toFIGS. 4A and 4B, the exemplary machines226may include a pair of opposing planar walls228that are connected by transverse walls230, which are semi-rigid or flexible, and have a curved shape. End walls231(FIG. 4) are located at each longitudinal end. The walls228and230together define a generally hourglass-shaped internal space232that is filled with one or more volumes of an incompressible fluid234(e.g., water, silicone oil, non-Newtonian fluids such as shear thinning fluids and shear thickening fluids, hydraulic fluid, and magneto rheological fluids) and one or more volumes of a compressible fluid236(e.g., air or another inert gas). When the planar walls228are subjected to compressive forces, the transverse walls230may bend and bow inwards into the internal space232and the compressible fluid236will be compressed to accommodate encroachment of the incompressible fluid234. In other implementations, the entire internal space232may be filled with a gas such as air. Alternatively, the entire internal space232may be filled with an incompressible fluid and the end walls231may be configured to bulge outwardly. Additional information concerning such dampers is disclosed in U.S. Pat. No. 6,830,793, which is incorporated herein by reference in its entirety.

The machines226are secured to arcuate member inner surfaces214aand216aand to the damper engagement device224. As the rod218and damper engagement device224moves back and forth, some of the machines226will be in tension and some of the machines will be in compression. As such, the machines226will not add or subtract to the positive spring constant K1. If on the other hand the machines were only located on one side of the damper engagement device224, then the spring constant of the machines would form part of the positive spring constant K1.

The positive and negative springs210and212are not limited to any particular springs, so long as the springs have the requisite positive or negative spring constants. Referring toFIGS. 5 and 6, and although the present inventions are not so limited, the exemplary negative spring212may be a conical disc238with stress-relieving cutouts240and242on the inner and outer diameters. Negative springs of this type are available, for example, from Associated Spring under the trade name Clover® Dome. Positive spring210is also a conical disc spring with stress-relieving cutouts on the inner and outer diameters in the illustrated embodiment. Positive springs of this type are also available from Associated Spring under the trade name Clover® Dome. As illustrated for example inFIG. 7, there are some instances where a negative spring will have a negative spring constant over only a portion of its load v. displacement curve. Here, the negative spring may be preloaded by, for example, selecting component dimensions, adding a spacer (note spacer244inFIG. 8) and/or adjusting the end caps220and222in such a manner that the negative spring is compressed into the portion of the load v. displacement curve that has a negative slope. It may also be desirable to prevent the negative spring from being compressed beyond the portion of the load v. displacement curve that has a negative slope. This may be accomplished by, for example, mechanical stops that prevent compression past a particular point or an overall damping apparatus configuration where, for the intended application, one would not expect displacement beyond the portion of the curve with the negative slope.

In some implementations, positive spring and motion damper functionalities may be performed by a common structure. For example, fluid fill machines such as those described above with reference toFIGS. 3 and 4may be used to provide positive spring and motion damper functionalities. One example of a damping apparatus with such an arrangement is generally represented by reference numeral200ainFIG. 8. Damping apparatus200ais substantially similar to damping apparatus200in form and function and similar elements are represented by similar reference numerals. For example, damping apparatus200aincludes a displacement conversion device202with a pair of arcuate members214and216, and a motion amplifier204awith a negative spring212, a rod218, and end caps220and222. Here, however, the damper engagement device224of the interface208ais not located between the arcuate members214and216and, instead, abuts the end cap220. A plurality of fluid-filled hourglass-shaped machines226, which function as both a positive spring and a damper, are located between the arcuate member outer surface214band the damper engagement device224. In particular, and referring toFIGS. 4A and 4B, the curved transverse walls230function as a positive spring and the compressible fluid236functions as a damper. It should also be noted that an annular spacer244is located between the negative spring212and the arcuate member216to support the outer rim of the negative spring away from the arcuate member so that the negative spring can compress.

Another exemplary damping apparatus is generally represented by reference numeral300inFIGS. 9 and 10. Damping apparatus300is substantially similar to damping apparatus200and damping apparatus200ain various aspects of their form and function, and similar elements are represented by similar reference numerals. For example, damping apparatus300includes a displacement conversion device302, a motion amplifier304, and a motion damper306. There is also a plurality of the above-described fluid-filled machines226, which have dual positive spring and damping functionality. Here, however, the displacement conversion device302has a half-leaf configuration with a planar member314and an arcuate member316. Such a configuration is better suited for vibration based displacement that tends to bend the damping apparatus300in the manner and direction identified by the arrows inFIG. 9. Such bending is about axis A3, which is perpendicular to both axis A1and axis A2, and results in some displacement in the directions of the first and second axes A1and A2. The motion amplifier304includes positive and negative springs and an interface, and creates an amplified displacement (as compared to the displacement along axis A2) at the interface. Here, the positive spring is defined by the transverse walls230(FIG. 4A) of the machines226that are located against and secured to the planar member inner surface314aand a damper engagement device324, and the negative spring312is carried on the arcuate member outer surface316b. The exemplary motion amplifier interface308has a rod318that extends through and is movable relative to the arcuate member316, a single end cap322that secures the negative spring312, and the damper engagement device324that is secured to (and therefore moves with) the rod318. Turning to the motion damper306, the exemplary motion damper includes a pair of dampers306athat act directly on the displacement conversion device302and are incorporated into K3, and a damper306bthat acts on the amplified motion associated with the motion amplifier304. In the illustrated implementation, the dampers306aand306bare each defined by the compressible fluid236(FIG. 4B) within the machines226. Here too, the damper engagement device324is a flat plate. In those instances where it is desirable to provide a flat surface for the machines226in dampers306a, a shim338with curved and flat surfaces may be provided.

The present vibration damping apparatus may be incorporated into (or used in combination with) a wide variety of systems and objects, as is described below with reference toFIGS. 11-20. The systems illustrated inFIGS. 11-20are presented for purposes of example only, and the present inventions are not limited to such systems and objects.

A structural plate, such as the structural plate400illustrated inFIG. 11, is one example of a vibration damping system that includes a plurality of the present vibration damping apparatuses. The exemplary structural plate400includes a plurality of individual vibration damping apparatuses200barranged in row and columns, i.e., end-to-end and side-to-side. Three rows of five damping apparatuses200bare shown in the illustrated embodiment. Systems with a single or column may also be provided. The damping apparatuses200bare essentially identical to the damping apparatus200in structure and function and similar elements are used to represent similar reference numerals. Here, however, the displacement conversion device202bin each apparatus includes ends tabs215and217where the arcuate members214and216are connected to one another. The displacement conversion devices202bare secured adjacent displacement conversion devices. Welding, adhesive, mechanical fasteners, or any other suitable instrumentality may be used to connect the damping apparatuses200bto one another. In other implementations, the arcuate member214(and/or the arcuate member216) for two, more than two, or all of the damping apparatuses200bmay be formed from a single piece of material that is sized and shaped so as to define a plurality of arcuate members. Other vibration damping apparatuses, such as damping apparatuses200,200aand300, may be employed in a structural plate in place of the damping apparatuses200b. Also, although the exemplary structural plate400employs a plurality of identical damping apparatuses, other structural plates may employ damping apparatuses that differ in one or more aspects. Also, a plurality of structural plates may be combined, e.g., into a T-shape or an I-beam.

A structural tube, such as the structural tube410illustrated inFIG. 12, is another example of a vibration damping system that includes a plurality of the present vibration damping apparatuses. The exemplary structural tube410includes a plurality of individual vibration damping apparatuses200positioned about the longitudinal axis LA. The first axis A1of each damping apparatus200is parallel to the longitudinal axis LA. The longitudinal ends of the damping apparatuses200are fixed relative to one another and, in the illustrated embodiment, are secured to anchor rings412and414. The structural tube410is intended to be oriented such that the longitudinal axis LA, and the first axes A1, are parallel to the vibration forces FVIB. Welding, adhesive, mechanical fasteners, or any other suitable instrumentality may be used to connect the damping apparatuses200to the anchor rings412and414. Other vibration damping apparatuses, such as damping apparatuses200a,200band300, may be employed in a structural tube in place of the damping apparatuses200. Structural tubes may also be formed from columns of vibration damping apparatuses that are secured to one another end to end. Also, although the exemplary structural tube410employs a plurality of identical damping apparatuses, other structural tubes may employ damping apparatuses that differ in one or more aspects. A bicycle seat post is one example of device that may be formed by the structural tube410.

A structural tube, such as the structural tube420illustrated inFIG. 13, is another example of a vibration damping system that includes a plurality of the present vibration damping apparatuses. The exemplary structural tube420includes a plurality of individual vibration damping apparatuses200cpositioned about the longitudinal axis LA. The first axis A1of each damping apparatus200cis tangential to the longitudinal axis LA. So configured, vibrational forces FVIBthat are perpendicular to the longitudinal axis LA cause displacement along the first axes A1of the damping apparatuses200c. The damping apparatuses200care essentially identical to the damping apparatus200band similar elements are used to represent similar reference numerals. Here, however, the displacement conversion devices202care relatively long in the direction parallel to the longitudinal axis LA, and include relatively long arcuate members214cand216cand end tabs215cand217c. Each damping apparatus200calso includes a plurality of motion amplifiers204and associated motion dampers206. Welding, adhesive, mechanical fasteners, or any other suitable instrumentality may be used to connect the damping apparatuses200cto one another. Other vibration damping apparatuses, such as damping apparatuses200,200a,200band300, may be employed in a structural tube in place of the damping apparatuses200c. Also, although the exemplary structural tube420employs a plurality of identical damping apparatuses, other structural tubes may employ damping apparatuses that differ in one or more aspects.

Other examples of vibration damping systems are grid systems such as the isogrid system430illustrated inFIG. 14. The exemplary isogrid system430includes a plate432and a plurality of triangular trusses434that are formed from damping apparatuses200. So arranged, the triangular trusses434perform a stiffening function as well as the above described vibration damping function. Vibrational forces acting on the plate432are transferred to the longitudinal ends of the damping apparatuses200, in the direction of axis A1, by way of the anchor posts436that define the corners of the triangular trusses434. The damping apparatuses200are connected to anchor posts436, but are not directly connected to the plate432. The plate432may be part of the structure whose vibrations are being damped, and the plate may be planar or curved. By way of example, by not limitation, a curved plate (or a plurality of connected curved plates) may define a cylindrical shape so that the structure may be employed in a rocket or other launch vehicle. Although the trusses434in the exemplary system430are equilateral triangles, the present systems are not so limited. Other patterns and arrangements including, but not limited to, squares, octagons and other geometric shapes, parallels, diagonals and combinations thereof (e.g., z-shapes), may be employed. Other vibration damping apparatuses, such as damping apparatuses200a-cand300, may be employed in the grid system in place of the damping apparatuses200. Also, although the exemplary isogrid system430employs a plurality of identical damping apparatuses, other systems may employ damping apparatuses that differ in one or more aspects.

Another exemplary grid system is the isogrid system440illustrated inFIG. 15. The exemplary isogrid system440includes a plate442and a plurality of triangular trusses444that are formed from damping apparatuses300a. The damping apparatuses300aare similar to apparatus300in form and function, and similar elements are represented by similar reference numerals. For example, each damping apparatus300aincludes a displacement conversion device302awith an arcuate member316, a motion amplifier304awith a negative spring312, a motion damper306awith a plurality of fluid-filled machines226that perform the positive spring and damping functions in the manner described above. A damper engagement device324ais secured to the motion amplifier interface rod (not shown). In contrast to damping apparatus300, however, the damping apparatus300aomits the planar member314(FIG. 9) and is configured to be mounted onto the surface of the underlying structure (e.g., the inner surface of the plate442). The ends of the arcuate members316are secured to the plate442by anchor posts446that define the corners of the triangular trusses444. The plate442may be planar or curved. By way of example, by not limitation, a curved plate (or a plurality of connected curved plates) may define a cylindrical shape so that the structure may be employed in a rocket or other launch vehicle. The machines226are located between the arcuate member316and the damper engagement device324a, and between the damper engagement device and the plate442. In other implementations, the machines226will be on only one side of the damper engagement device324a. Although the trusses444in the exemplary system440are equilateral triangles, the present systems are not so limited. Other patterns and arrangements including, but not limited to, squares, octagons and other geometric shapes, parallels, diagonals and combinations thereof (e.g., z-shapes), may be employed. Other vibration damping apparatuses, such as damping apparatuses200-200cand300, may be employed in the grid system in place of the damping apparatuses300a. Here, the anchor posts446would also provide a spacing function to suspend the damping apparatuses relative to the plate442. Also, although the exemplary isogrid system440employs a plurality of identical damping apparatuses, other systems may employ damping apparatuses that differ in one or more aspects.

Other examples of vibration damping systems are strut systems, such as the strut system452in the payload attach fitting (or “forward adapter”)450illustrated inFIG. 16. The strut system452includes a plurality of struts454, and each strut includes a plurality of damping apparatuses200b. Other aspects of the payload attach fitting450include the payload interface456and the spacecraft interface ring458which are located at opposite ends of the strut system452. The struts454are connected to anchors460and462on the payload interface456and spacecraft interface ring458. The vehicle fuel tank466is also visible inFIG. 16.

Other examples of vibration damping systems are braced-frame systems, such as the braced-frame system470illustrated inFIG. 17. The exemplary braced-frame system470includes horizontal and vertical frame members472and474, and braces476. Vibration damping apparatus, such as damping apparatus200, may be positioned in series with the braces476(e.g., at the longitudinal ends of the braces) and/or in parallel with the braces476(e.g., structural plates400that are coextensive with braces), and/or in series or parallel with the frame members472and474. The damping apparatuses200may be configured to dampen low-amplitude vibrations before the remainder of the braced-frame system470acts on large amplitude motions.

Turning toFIG. 18, the present vibration damping systems also have application in reinforced concrete shear walls. The exemplary shear wall480illustrated inFIG. 18includes a concrete wall482mounted on a frame484. Structural plates400may be embedded within the concrete. The structural plates400which may be oriented horizontally, vertically or at an angle in between (as shown), are stiffer than the concrete and therefore attract (and damp) vibrations.

Another exemplary application is boat hulls. The exemplary boat hull490illustrated inFIG. 19incorporates one or more of the present vibration damping apparatus and/or systems. To that end, the exemplary boat hull490consists of an internal network of frames (not shown), that extend from side to side and that run the length of the boat, that are covered by an outer shell492(e.g., fiberglass or metal). Other boat hulls consist solely of the outer shell. The frames and/or shell may be formed from one or more of the above-described vibration damping apparatus and/or systems. The apparatus and systems illustrated inFIGS. 9,10and15are especially applicable to the outer shell of a boat hull.

The exemplary airplane wing500illustrated inFIG. 20also incorporates one or more of the present vibration damping apparatus and/or systems. The exemplary wing500may include an external skin502and internal structures (not shown) such as ribs, stringers and spars. The external skin502and/or the internal structures may be formed from one or more of the above-described vibration damping apparatus and/or systems. The apparatus and systems illustrated inFIGS. 9,10and15are especially applicable to the external skin of an airplane wing.

Although the present inventions have been described in terms of the preferred embodiments above, numerous modifications and/or additions to the above-described preferred embodiments would be readily apparent to one skilled in the art. It is intended that the scope of the present inventions extends to all such modifications and/or additions.