Background of the Invention As sporting equipment has become a major industry, it has become increasingly important for manufacturers to be able to tailor the"feel"of this equipment in use. One of the major factors affecting user perceptions of many types of sporting equipment is that equipment's vibration characteristics. Many users prefer that sporting equipment minimize levels of shock, vibration, and airborne noise. The first two quantities are particularly important in determining performance and feel of many kinds of sports equipment, e. g., aluminum baseball bats, golf clubs (primarily the shafts), tennis rackets, skis, and snowboards. The last quantity, airborne noise, is important for equipment that involves impact and psycho-acoustic feedback to the user such as aluminum baseball bats and golf clubs (primarily the heads).

Reduction of structural vibration is also desirable for wheeled sports equipment, such as motorcycle frames, off-road two, three, and four wheel vehicle frames and chassis, and in bicycle frames. Some types of non-wheeled sports equipment, such as snowmobiles and personal water-craft, are also prone to structural vibration. In all of these applications, a reduction of the level of structural vibration would improve the quality of the ride for the user, which has a number of benefits, including reducing fatigue and increasing safety. Reduction of structureborne vibration is also important for sports vehicles, where continuous excitation of frames and chassis radiate sound to the user and others.

Granular materials represent attractive candidates for use as damping materials in sporting applications, because of the ease of fabrication of equipment incorporating these materials. For example, a granular material can simply be poured into a hollow shaft of a golf club during fabrication.

For decades, sand and lead shot have been used as a damping treatment, but both are relatively dense, and thus result in a large weight penalty. In a golf club, for example, the reduction in user fatigue and discomfort due to reduction in"sting" associated with a shaft filled with lead, would be offset by the increase in fatigue associated with the increased weight of the shaft. Further, the heavier shaft would result in a reduced impact velocity and spin imparted to the ball for a given user effort, and thus would degrade the performance of the club. It is generally recognized in the art that light weight is desirable in many types of sports equipment, particularly in equipment which is meant to sustain impacts (e. g., golf clubs, baseball bats, and tennis rackets).

Other suggested granular materials for damping are viscoelastic spheres, which have the advantage of generally being of lower density than sand or lead shot, but whose damping characteristics are temperature sensitive, since the viscoelastic properties of the sphere material are strong functions of temperature. The resulting variability in"feel"would degrade performance from a user standpoint. In the case of skis and other winter sports equipment, the difference in feel between a heated store environment during purchase and the much colder environment of use would be a severe impediment to user satisfaction.

A need thus exists for a low-density, granular material whose vibration damping properties are substantially insensitive to temperature, for use in sporting equipment. Ideally, such a material should be lightweight, with good damping properties, ease of manufacture, and low cost. It is an object of the present invention to supply this need.

Summary of the Invention In one aspect, the invention comprises a piece of sporting equipment, such as a ski, snowboard, golf club, baseball bat, or sports vehicle, the equipment comprising a granular material for vibration damping. The granular material is coupled to the structure in order to damp vibrations incurred during the use of the sporting equipment for a sports activity. These vibrations may represent structureborne vibrations in the equipment, or airborne noise produced by the equipment. In the embodiment of a damped ski, the granular material may be disposed between epoxy

laminates of the ski. In the embodiment of a damped golf club, the granular material may be disposed in the normally hollow portion of the shaft, and/or it may be disposed in the head of the club. In the embodiment of a baseball bat, the material may be disposed in the hollow interior of the bat. A preferred bat for this embodiment is made of aluminum. In the embodiment of a sports vehicle, the vehicle may be any of a bicycle, a motorcycle, an all-terrain vehicle (ATV), a snowmobile, or a personal watercraft. In all of these embodiments, the granular material is of low density (below about 1000 kg/m3), or is of low bulk sound speed (less than about 90 m/s), or is nonsolid (ie., the individual granules comprise voids). The materials may also be nonspherical (e. g., dendritic materials) and/or nonplastic (e. g., glass, vermiculite, perlite, ceramic foams, metal foams, and flock). Preferred damping materials are low-density polyethylene, glass microballoons, perlite, vermiculite, expanded polystyrene, flocking, and combinations thereof. Further, the granular material may be selected so as to be substantially insensitive to variations in temperature. For example, for winter sports equipment, the damping may be substantially constant over the temperature range-20 to 0°C, or preferably-20 to 30°C.

In another aspect, the invention comprises a method of reducing vibrations in sporting equipment, such as skis, snowboards, ski poles, golf clubs, tennis rackets, baseball bats, or sports vehicles. The method comprises coupling the equipment to a granular material which damps vibrations caused by use of the equipment for a sports activity, the granular material being of low density (below 1000 kg/m3), of low bulk sound speed (less than 90 m/s), or nonsolid (e. g., hollow spheres or foam particles).

The material may comprise nonspherical granules (e. g., dendritic granules) and/or nonplastic granules. The damped vibrations may represent structureborne vibrations in the equipment, or airborne noise produced by the equipment. The granular material may be selected to render the damping substantially independent of temperature.

In still another aspect, the invention comprises methods of mechanically annealing structures comprising granular materials. The mechanical annealing comprises subjecting the structure to an acceleration or shock which causes the vibration damping characteristics of the material to improve. For example, the transfer mobility of a force input may be reduced at at least one vibration frequency.

The granular material may be a dendritic material such as flocking, and it may be packed to a level greater than or equal to the optimum packing density for the system.

The sound speed of the granular material may be below about 100 m/s, or preferably below about 90 m/s, and the material may be low density (e. g., below about 1000 kg/m3). The method may include subjecting the structure to repeated shocks until no further improvement of the damping properties is gained. In a related aspect, the invention comprises a piece of sporting equipment subjected to this mechanical annealing procedure.

As the phrase is used in this application,"LodengrafrM materials"'are granular materials intended for use for vibration damping."LodengrafrM damping" refers to methods of vibration damping comprising coupling LodengrafrM materials with at least a portion of an article subject to vibration.

As the phrase is used in this application, the"sound speed"of a granular material refers to its bulk sound speed in its granular form.

Brief Description of the Drawing The invention is described with reference to the several figures of the drawing, in which, Figures la-11 portray various pieces of sporting equipment which can be damped according to the invention: respectively, a golf club shaft, a golf club head, a ski, a baseball bat, a bicycle, a motorcycle, an all-terrain vehicle, a personal watercraft, a snowmobile, a snowboard, a ski pole, and a tennis racket; Figure 2 portrays a comparison of the drive point accelerance for a ski damped according to the invention and an undamped ski; Figure 3 portrays a comparison of the transfer accelerance for the shaft of a golf club damped according to the invention, a shaft damped by a viscoelastic material, and an undamped shaft; Figure 4 portrays a comparison of the transfer accelerance for the shaft of a golf club damped with rayon flocking material at several packing densities; '"Lodengraf'is a trademark of Edge Innovations & Technology, LLC, the assignee of this application.

Figure 5 portrays a comparison of the transfer accelerance for the shaft of a golf club damped with rayon flocking material and'subjected to 0,1,2, or 3 mechanical annealing steps; Figures 6a-6c portray comparisons of the vibrational response of an aluminum bat damped according to the invention and an undamped bat; Figure 7 portrays a comparison of the accelerance for an aluminum tube damped according to the invention and an undamped tube; Figure 8 portrays a comparison of the accelerance for an aluminum plate damped according to the invention and an undamped plate.

Detailed Description Low density granular damping materials, also known as LodengrafrM materials, have been shown to be effective in reducing structural vibrations and associated airborne radiation in a number of application areas. In particular, these materials can be advantageously used to reduce such vibration in sports equipment, such as baseball bats, golf clubs, tennis rackets, skis and snowboards, and personal recreational vehicles such as motorcycles, ATVs, bicycles, snowmobiles, and personal watercraft. Several such applications of these damping materials are illustrated in Figures la-11. The LodengrafrM materials may be disposed in a hollow space in the equipment, encapsulated in a pouch which is affixed to the equipment, or mixed with a small amount of adhesive to form a free-standing shape which can be attached to the equipment.

LodengrafTM materials can be incorporated into all of these types of sporting equipment in order to reduce vibration and associated airborne noise. Different types of LodengrafrM materials will be appropriate for different applications. Typical vibration sources for sporting equipment are (i) impacts and (ii) vibration associated with motors. The vibration source and the material which transmits vibration to the user will have a strong impact on the spectrum of vibration experienced. In general, it is found that low-frequency vibrations are more difficult to damp than high-frequency vibrations.

Current understanding of LodengrafrM damping physics is based upon the physical process of radiation from structureborne vibration into the granular material.

Historically, sand and lead shot granular materials have been used for damping, but significant weight penalties accrue with their use. The present inventor has shown that it is the low sound speed of the granular material that enables and accentuates the process of radiation into LodengrafrM material from the vibrating structure. Many granular fill materials have been tested to date of which a few are shown in Table 1. Examples of measured results for a few specific sports applications are reviewed in the following sections. Lodengrafi'M material sound speed density code (mls) (kglmj) L-KO150 3M ScotchliteTM glass 97 70 microballoons L-E3000 expanded polystyrene 96 11 (EPS) L-L4000 low density polyethlene 95 570 (LDPE) L-V3000 vermiculite 90 132 L-P20L80 20% perlite/80% LDPE 67 475 L-P5000R perlite 62 97 L-P 1500 processed perlite N/A 200 L-P50L50 50% perlite/50% LDPE 56 334 L-P40L60 40% perlite/60% LDPE 56 381 L-P60L40 60% perlite/40% LDPE 54 286 L-P80L20 80% perlite/20% LDPE 51 192 L-P43S57 43% perlite/57% sand 37 931 L-R0030 3 denier, 0.030"-100-200 precision cut rayon flock (unannealed) L-N0020 3 denier, nom. 0.020" N/A-200 random cut nylon flock Table 1

Nonspherical particle morphologies are preferred for the damping materials of the invention, because ideal sphere packings have particularly stiff bulk moduli, which are associated with higher bulk sound speeds.

Two of the materials shown in Table 1, the rayon and nylon flock materials L-R0030 and L-N0020, have unexpectedly been found to produce good damping performance despite relatively high measured sound speeds. It has been found that the damping performance of flock and other materials can be enhanced by mechanical annealing, as described below. It should be noted that the measured sound speed listed in Table 1 for L-R0030 is for an unannealed specimen; the annealing process is expected to reduce sound speed significantly. The sound speed of L-N0020 has not been measured, but the damping characteristics of L-R0030 and L-N0020 have been measured and found to be extremely similar, suggesting that their sound speeds are also similar.

When installing LodengrafrM granular materials into equipment it is often desirable to eliminate any rattle and material movement. The rattle can be distracting in use, and reduces the sound quality of the product. Eliminating granular particle movement of the material promotes reduced rattling (and thus reduces extraneous noise), but also enables the product to conform to certain regulatory constraints imposed by various sports governing bodies. In addition to the elimination of particle movement, the choice of material is critical in reducing extraneous noise: softer LodengrafrM materials being preferred for this situation.

Increased packing density, however, tends to produce increased local stresses in the material, essentially pre-stresses, that reduce the effectiveness of the damping treatment. These local stresses are due to bridging or arching of the granular material, which produces structurally stiff"short-circuits"connecting distant points. This results in a globally stiffer material, which in turn, increases the bulk material sound speed since c2=K/p, where c is the material sound speed, K is the material bulk modulus, and p is the material density.

As discussed herein, low sound speed is the feature of LodengrafrM materials that enables and accentuates damping of structureborne vibrations. Thus increased packing to eliminate particle movement produces increased pre-stress in the material, which increases the bulk sound speed and adversely affects the damping performance.

It is therefore very desirable to eliminate the internal material pre-stress and thereby regain the damping performance, but to do so without reducing packing density, i. e., to preserve the condition of no macroscopic particle motion. It has been found that this goal may be achieved by mechanically annealing the LodengrafrM material after an optimum packing density has been achieved. Optimum packing density is considered to be the"fully-packed"density: the lowest density at which motion of the damped structure will not produce bulk motion of the damping material. The mechanical annealing processes described herein are effective for packing densities equal to or greater than the optimum packing density.

The mechanical annealing process achieves an effect similar to the effect of thermally annealing a metal to reduce the residual stresses associated with cold work.

Annealing is accomplished by subjecting the LodengrafrM material to high accelerations or shocks, such as those associated with impacts. These accelerations serve to break up arches and bridges in the granular material, thereby reducing local stiffness concentrations and improving damping performance. The annealing process is described below in connection with using flock materials to damp vibration in golf clubs, but it is also applicable to the other types of sporting goods and granular materials disclosed in this application. It is expected that the annealing process will be especially useful in conjunction with flexible, highly dendritic granular materials such as flocking. These materials have the property of being packable in a wider range of densities than more traditional granular structures such as sand or shot. The annealing processes of the invention are applicable to materials packed at a range of different densities, but higher packing densities may require higher accelerations in order to achieve annealing. The optimum packing density is considered to be the lowest at which the granular material does not move globally within the structure under acceleration of the structure. (Local movements associated with breaking arches and bridges will of course occur during the annealing process).

Skis and Snowboards Ski and snowboard equipment undergo enormous shock and vibration loads, particularly in high speed conditions on hard or icy snow. Skis and snowboards are essentially cantilevered beams on elastic foundations (the snow) with clamped, or at

least relatively high impedance, boundary conditions at the bindings and virtually free boundary conditions at the tips. With high impact loads and relatively low damping, shock from impact is transmitted to the user's feet, and oscillations develop in the skis or snowboards. In addition, skiers also use ski poles, which are also subject to vibration upon impact with the snow during turns.

Vibration causes fatigue and, if sufficiently intense, loss of control over the snow. One of the advantages of LodengrafrM materials is their ability to reduce structural vibrations over a broad range of temperatures where conventional viscoelastic materials lose performance. At high temperature viscoelastic materials become limp and if loaded will ooze or sag. At low temperatures they will become stiff and no longer provide effective damping. LodengrafrM materials, on the other hand, do not rely on viscoelasticity and thus can be designed to meet vibration reduction needs at both high and low temperatures. For the ski and snowboard equipment application, it is the low temperature range that is of importance.

An example of the Lodengrafl'M damping performance on a ski is shown in Figure 2. This set of curves shows the drive-point accelerance (acceleration per unit force) for the forward end of a cantilever ski clamped at the toe binding position. The light curve 50 shows the response of an undamped ski, while the heavy curve 52 shows the response of the damped ski. The LodengrafrM damping used was a layer of L-L4000 material (based on low-density polyethylene (LDPE) beads) applied to the forward end of the ski using a shrink wrap plastic cover. Peaks in the curves correspond to resonant frequencies at which motion of the ski is high.

The important frequency range for tactile response of humans is below 700- 800 Hz for high amplitude motions. The damped curve 52 of Figure 2 shows three strong peaks at about 450,610, and 850 Hz that are reduced by 5-10 dB, compared to the undamped curve 50. The resonant peaks at about 25 and 110 Hz are reduced by 3-4 dB, while the peak at 200 Hz is slightly increased. The lower frequency resonant peaks are affected less than the higher frequency peaks using the LDPE treatment.

The incorporation of other materials with a lower sound speed is expected to lead to greater reduction of the lower frequency peaks.

Installation of LodengrafrM material into a ski or snowboard can be accomplished by first forming the material in a pouch of the desired shape. The pouch

is then vacuum sealed and incorporated into epoxy laminant that make up the typical ski structure. This configuration is illustrated in Figure lc for a ski 18 comprising a layer of damping material 22. Any of a broad range of LodengrafrM materials can be used in construction depending on the level of damping needed for the particular design.

LodengrafrM materials could also be used for vibration damping in ski poles, using substantially the same disposition of material as that described below in connection with the shafts of golf clubs. As with skis and snowboards, the temperature insensitivity of selected Lodengraf materials makes them particularly advantageous when used to damp vibration in ski poles.

Golf clubs When a golf club impacts a ball, the acceleration level at the club head is thousands of g's and force levels are of the order 10,000 N. These loads produce shock that excites vibrational modes in the golf club shaft and propagates to the player's hands producing sting, discomfort, and fatigue. This shock can also contribute to repetitive use injury. Reduction of such shock and vibration has been attempted in many ways without success. One of the recent commercial products released to address this problem is Sensicorew2 by True Temper, Inc. The SensicoreTM shaft comprises a helical piece of viscoelastic material wrapped around a hollow core and disposed in the shaft of the club. This shaft is compared to a Lodengraf damped driver shaft in Figure 3.

In Figure 3 the dynamic responses of three shafts are compared. The shafts are all driver shafts of the same length, 45", and approximately the same weight, 122g.

Each was hung from a rubber band suspension (with a 7 Hz resonant frequency) to approximate a free-free beam. Transfer accelerance measurements (acceleration per unit force) were taken with the force applied at the tip end of the shaft and acceleration received at the butt end. This configuration approximates the excitation and sensing location of a golf club in use. In Figure 3 the light line 54 is the undamped shaft, the dashed line 56 is the SensicoreTM shaft, and the heavy line 58 is 2 SensicoreTM is a trademark of Emhart, Inc.

the response from a shaft identical to the undamped shaft except it has been filled with a Lodengrafrm L-P5000R material (based on perlite, an expanded volcanic siliceous glass). The incremental weight for the added material was 13.5g compared to an empty shaft weight of 122.5g. The experimental results clearly show the effectiveness of the Lodengraf treatment, even at a frequency of 275 Hz. Note that the first resonant frequency affected by the Sensicore treatment is at about 950 Hz, while the Lodengraflm treatment reduces peaks by 5-10 dB for all resonant peaks above 275 Hz.

A particular configuration of Lodengrafrm material 12 for damping the shaft 11 of a golf club 10 is illustrated in Figure la. The head 14 of the club could also be damped with Lodengrafrm material 16, as illustrated in Figure 1 b. To facilitate manufacturing, inserts containing the LodengrafrM material can be fabricated separately then dropped into the shaft as part of the construction process. The inserts can be made by forming a plug of chosen LodengrafTm material, depending on the level of damping needed, then vacuum sealing the material within a pouch of thin polyethylene or rubber. Just prior to installing the insert into the shaft an adhesive can be applied to the insert or the interior of the shaft. Application methods for the adhesive include spray, brush, and dipping. The adhesive should be designed to be a lubricant when it is first applied, facilitating insertion into the shaft, and then it should form a flexible bond to the interior of the shaft when it dries (or cures). It may be desirable to puncture the pouch containing the LodengrafrM material after it has been installed in the shaft to release the vacuum. Other installation procedures might include the use of short (1/2"-1") foam plugs at both ends of the insert to insure the Lodengrafrm material remains in place.

Optimum packing and subsequent annealing of the LodengrafTm material is essential for certain materials, to eliminate rattle or material particle motion while preserving superior damping performance. An example of the effects of increased packing density is shown in Figure 4 where the L-R0030 Lodengraf rayon flock has been installed into a golf club shaft. This is a soft material that was chosen to eliminate rattle sounds which occur when harder materials, such as the L-P5000R LodengrafTm perlite granules, impact on the inside of the shaft. The dashed line 80 in Figure 4 corresponds to the response of an undamped golf club shaft, while solid lines

82,84,86, and 88 represent the response of damped shafts packed with unannealed L-R0030 to densities of 0.20,0.22,0.24, and 0.26 gfcm3, respectively.

The experimental setup resulting in the transfer mobility curves (acceleration per unit force) of Figures 4 and 5 was identical in both cases. In each case a golf club shaft (True Temper X100,37"shaft) was suspended by elastic mounts in a horizontal position. The suspension frequency was about 8 Hz as may be seen by the consistent peak in the responses near that frequency. The elastic mounts were positioned at 15 cm from the two ends of the shaft. Acceleration measurements were taken with an accelerometer at a position 7.5 cm from the butt end of the shaft and an impact hammer provided force input 3 cm from the tip end of the shaft. This geometry was chosen to approximate that of a golf ball being struck near the tip of the shaft (force) and a player's hands being positioned near the butt (acceleration). Transfer mobility was computed using the ratio of output acceleration to input force and displayed in units of dB relative to kg-'. The analysis bandwidth was 1.6 kHz with 800 lines or 2 Hz resolution. Each curve on the plots is the vector average of five individual transfer mobility measurements. High levels of transfer mobility indicate high levels of dynamic excitation on the shaft. Thus reducing the peak levels as shown in these figures is the goal of the damping.

The range of human tactile sensitivity is below about 700-800 Hz, thus the three major peaks at about 80,240 and 450 Hz are the principal peaks of interest.

Reduction of these peaks through the application of Lodengraf materials corresponds to reductions in the dynamic response felt by the user.

In Figure 4 it is clear that as packing density increases, the damping effects of the Lodengrafw treatment decrease when no subsequent annealing has been performed. This is evident by the increasing level of the transfer mobility peaks corresponding to the increasing level of material packing. Note particularly the one- to-one correspondence in the peaks around 240 Hz between damping level and packing density.

For the L-R0030 LodengrafrM rayon flock material the optimum packing density is p=0.26 gm/cm3. At this level of packing there is no macroscopic motion of the material, but annealing can be performed to produce significant damping, as will be shown below. Greater packing densities also result in no macroscopic motion, but

the imposed internal stress concentrations are sufficiently high that annealed damping levels are not as effective as those for a packing density of p=0.26 gm/cm3. The optimum packing density is a tradeoff between the elimination of macroscopic motion and satisfactory damping performance achieved through annealing. Further, optimum packing density is a function of the material chosen and must be determined through experimentation.

Figure 5 shows the effects of annealing for the L-R0030 LodengrafrM rayon flock with a fixed packing density of p=0.26 gm/cm3. The figure also shows the dynamic response of the undamped shaft for comparison. Once the desired packing density is achieved by tapping and filling in any given installation, the structure is plugged to prevent the LodengrafrM material from migrating. Annealing is then achieved by further tapping with blows sufficiently sharp to produce high acceleration levels within the structure and break the internal material arches and bridges. With the golf club shaft, which was used for the results shown in Figure 5, the annealing was done by dropping the shaft flat on a hard surface from height of a few inches.

Permitting the tip end or the butt end to hit first promotes differential accelerations within the structure that may promote breaking of the internal material arches and bridges. Figure 5 compares the effects of annealing the LodengrafrM material one, two, or three times. Dotted line 80 represents the response of the undamped shaft, while solid lines 88,90,92, and 94 show the responses of shafts packed to a density of 0.26 g/cm3 and annealed 0,1,2, and 3 times, respectively. There is a point of diminishing returns between the second and third annealing step, which suggests that most of the material pre-stress has been relieved. Annealing may be achieved in a variety of ways during manufacturing, but in all cases the process must result in acceleration levels sufficiently high to break the internal, high-stiffness arches and bridges within the material.

In many types of sports equipment, including golf clubs, annealing will be a natural process that occurs via high-energy impact during normal use of the product.

Damping performance of the equipment will be maintained in the equipment through a continuous self-annealing process. As evident upon analysis of the data presented in Figure 5, this self-annealing process will result in reductions to a certain damping level, then subsequent use will simply maintain that level of performance.

While the description of optimum packing and annealing associated with Figures 4 and 5 has been specific to golf club shafts, the same principles are applicable to all of the sporting equipment of this invention. Extensions of this damping technique for other sports applications will be apparent to those skilled in the art given the description above relating to golf club shafts.

When filling with flocking material as described above, a decision must be made as to the optimal specific gravity for filling. Different golf club shafts will require different amounts of material if the same shaft length is to be filled.

Alternatively, manufacturing may be easier if the shafts of different lengths are filled to varying depths in order to keep the mass of damping material constant. Table 2 shows exemplary filling depths for a set of DGIS400 shafts of lengths from 35-39 inches. The shafts are filled with 10 g of rayon flock material, packed to an optimum specific gravity of 0.26 g/cm3. For manufacturing purposes, 10 g of flock are poured into the shafts, and plugs are inserted to the specified depths to contain the LodengrafrM material in the shaft. The fill depths vary because of differences in degree of taper and tip length in the shafts. Shaft length (in) Fill depth (cm) 35 34.4 35H 34.9 36 35.4 36H 36.1 37 36.7 37H 37.4 38 38.0 38H 38.6 39 39.2 Table 2

Baseball bats One of the most difficult challenges amateur baseball players face when moving into the major leagues is getting used to the wooden bats. Roughly two generations of ball players have learned their hitting skills using aluminum bats, which have a characteristic"ping."This sound masks the psycho-acoustic feedback of the ball-bat impact delivered to the player. Another major difference is the feel of the aluminum bat, which exhibits greatly reduced intrinsic damping compared to a wooden bat. With lower damping, a hit away from the"sweet spot"produces significant sting (structureborne vibration) on the player's hands. Both of these effects can be addressed with the use of Lodengraf material within the bat as shown in Figures 6a-6c. To make these measurements a commercial 28 oz. aluminum softball bat was filled with a LodengrafTM L-KO150 material (based on 3M ScotchliteTM glass microballoons). The additional weight was 2 oz. A bat intended to be used in conjunction with LodengrafrM materials could be made somewhat lighter, so that the bat filled with Lodengrafl'M material was of regulation weight.

Figure 6a shows two time series of the airborne acoustic impact sounds between the bat and a tossed softball. The light curve 60 shows the results from the unmodified bat and the dark curve 62 corresponds to that of the modified bat. Note in both curves that the initial ball-bat impact produces a sharp impulsive signal with a period of roughly 2.5 ms, which corresponds to a center frequency of about 400 Hz.

For the case of the undamped bat, a modulated ringing sound begins immediately but, due to directivity effects of the bending waves on the bat and the position of the microphone, does not reach its peak amplitude until a time of about 40 ms. The frequency of the ping is roughly 2700 Hz and corresponds to a strong bending mode of the bat. This is the characteristic"ping"of an aluminum bat. Actually, two modes are excited with a separation of about 500 Hz, which is what produces the modulation (beating) effect seen in the unmodified bat response. As can be seen in Figure 6a, the ping sound in the bat modified with the Lodengafrm material is completely absent.

Figure 6b shows the same information in the frequency domain. The unmodified bat response is shown as the light line 64, and the modified bat response as the dark line 66. Note that the ball-bat impact portion of the spectra 64 and 66 is very similar, apart from a slight change in amplitude due to differences in how hard the ball was

hit. The striking difference is seen in the total elimination of the two"ping"tones at 2400 Hz and 2900 Hz. The LodengrafrM treatment has reduced the level of the ping tones by 20-25 dB and completely removed their contribution from the spectral response.

Figure 6c shows a structureborne vibration response of the same bat. The experiment is similar to the golf club shaft experiment described above. The bat was hung from elastic supports and transfer accelerance measurements (acceleration per unit force) were taken with force in the vicinity of the bat's"sweet spot"and the accelerometer near the player's grip. The dashed curve 68 shows the response of the unmodified bat, while the solid curve 70 shows the response of the bat filled with Lodengrafrm L-K0150 material. The lowest order mode at about 250 Hz is reduced by about 2 dB, while all the higher order modes at 700,1300, and 2000 Hz are reduced by 15-30 dB. Reduction of the two lowest order modes improves the feel of the bat. Reduction of the higher order modes eliminates the bat ping, which provides for better bat-ball impact psycho-acoustic feedback to the player.

In the manufacturing process, the bat can be completely filled, or alternatively, it can be partially filled with plugs holding the damping material in locations of greater structural dynamics. A bat 24 damped according to the invention is illustrated in Figure ld. LodengrafrM material 26 is disposed in the center of the bat 24. As with the golf club shafts, inserts to hold the LodengrafrM material can be constructed separately and inserted at the time of final assembly, or the bats can be filled with loose Lodengraf material directly.

Sports vehicles Shock and vibration transmitted to the user of sports vehicles, particularly off-road vehicles, produce fatigue and injury. Vehicles including human powered devices, such as bicycles, as well as motorized vehicles, such as motorcycles and snowmobiles, are all subject to high impact loads due to maneuvering in rough terrain. In addition, motorized vehicles whether on-or off-road transmit vibration from the motor and drive train to the user. In all cases, the path of transmission is directly or indirectly through the frame of the vehicle, which is generally a structure composed of beam-like and plate-like components. A particular configuration of

LodengrafrM damping materials employed in a bicycle 28 is illustrated in Figure 1 e.

Damping material 32 is disposed within a tubular member 30 of the bicycle frame.

More damping material 36 is disposed along plate-like members in the solid front wheel 34 of the illustrated bicycle, and also at the wide-spoked rear wheel 40. The damping material may be disposed inside a hollow space in a member, or it may be encapsulated into a pouch which is secured to the member. This pouch may be"one- sided,"that is, it may comprise a sheet of plastic or other suitable material affixed to the member, and the granular material may then be poured into the space between the pouch and the member. In another configuration, the material may be mixed with a small amount of adhesive, so that the grains of the material will maintain a shape without need for encapsulation into a pouch or hollow space in the equipment.

LodengrafrM treatment of beam-like and plate-like structures has been shown to significantly reduce vibration levels as shown in Figure 7 for a tubular beam structure, and Figure 8 for a plate structure.

The beam structure was an aluminum tube with an OD of 12.7 mm, a wall thickness of 1.5 mm, and a length of 46 cm. Drive point accelerance measurements (acceleration per unit force) were taken at the end of the beam with and without damping. The damping material was LodengrafrM L-P1500 and it completely filled the damped beam. Figure 7 shows the results with the lowest order mode at about 350 Hz being reduced by 7 dB and the next mode at about 850 Hz being reduced by 15 dB. The light line 72 represents the undamped beam, and the heavy line 74 represents the damped beam. The higher order vibrational modes are reduced by even greater amounts, but they would not contribute to any tactile difference as felt by the user.

The reduction of these higher order modes would, however, reduce the radiated noise from the structure.

The plate structure was an aluminum sheet 101/2"x 15l/2"with a 1"turned lip around the edge. The sheet thickness was 1 mm. Averaged transfer accelerance measurements (acceleration per unit force) were taken using a single accelerometer receive point and three force excitation points on the plate. Figure 8 shows the results of the measurements for an undamped (light line 76) and a damped (dark line 78) plate. The damped plate was treated with a LodengrafrM L-L4000 material held in place using shrink wrap film. The transfer accelerance is reduced by 20-30 dB over a

range of frequencies from about 200 Hz and up. These reduced accelerance levels would contribute to reduced vibration sensed by the user as well as reduced acoustic radiation. Plates are notorious for radiating sound, and LodengrafrM treatments would have a significant impact in reducing the noise created by plates coupled to vibrating vehicle components.

The above-described applications of LodengrafrM materials to vibration damping in sports equipment are intended to be exemplary, and to provide guidance as to principles for selection and application of damping apparatus for particular systems. Other methods of application of LodengrafrM materials to the damping of vibration in sports equipment, whether to the particular types of equipment described above or to other equipment types, and whether using the specific materials described above or other LodengrafrM materials, are also included in the present invention, whose true scope and spirit is indicated by the following claims.

What is claimed is: