* Senior Staff Engineer, Dynamics Dept., One Space Park, MS:R4-1104

Particle Damping Applications

Stepan S. Simonian*

Northrop Grumman Space Technology, Redondo Beach, CA. 90278

Particle damping is a generalization of impact damping technology (also known as acceleration dampers), but also provide additional damping mechanisms when compared with other kinetic energy based vibration dissipation devices. Due to their inherent design simplicity, in recent years there has been considerable interest in this technology. Most of the reported results have been obtained empirically, however, recently there has been some activity in the construction of analytical/numerical models to simulate the energy dissipating performance of particle dampers. The work described in this paper documents experimental work and representative test results of various particle dampers used to suppress excessive vibration of cantilever type space structural subsystems of various sizes subjected to transient and steady-state vibratory disturbances. It is experimentally demonstrates that the performance of these devices are highly amplitude dependant. It is also experimentally shown that there are three distinct damping performance regions for transient type excitations. In addition to partially filled cavity particle dampers, other particle dampers are also investigated such as particles-in-ball and preloaded particle dampers. In its simplest form, a particle damper consists of a cavity box of various shapes and sizes that are partially filled with particles. Particles can be metallic, ceramic, polymeric, composite or a mixture of various materials. The particle size may vary from application to application and may vary from a few micro-inches to a tenth of an inch or more. The shape of the particles may be near spherical, cylindrical or irregular in shape. The shape, size and material of the particles will influence flow characteristics of the particles in the cavity. Other particle damper configurations are also experimentally studies. In one configuration a polymeric ball is partially filled with particles. The ball is then placed in a cavity that is secured to a vibrating structure. The vibration sets the ball in motion in the cavity. Since the ball is only partially filled with particles, any rolling action of the ball will set the particles in motion against one another and maintain a new surface level, similar to a fluid leveling itself to maintain equilibrium due to gravity. The ball will eventually collide with cavity walls thus functioning as an impact damper with additional frictional losses due to particle friction and other losses due to elastic/plastic deformation of particles and the polymeric material of the ball. In another application, the particles are placed in a confined elastic cavity such as a metallic bellows or a rubber tube and sealed at the ends. The elastic walls of the rubber tube will induce compressive forces on the particles as more and more particles are stuffed into the tube. The amount of particles in the elastic cavity will determine the amount of preload on the particles. Any bending action of the particle filled elastic tube will be accompanied with relative rubbing motion among the particles, thus dissipating energy by dry friction.

I. Introduction

In recent years interest in particle mechanics has grown significantly mainly due to the importance of

particulate matter in a number of industries such as agriculture, mining, pharmacology, etc. It has been shown mainly by the physics community1, 2 that an assemblage of non-cohesive particles displays a rich array of dynamic and wave propagation phenomena when exposed to dynamic environments. Some early studies3,4,5 have demonstrated the usefulness of an assembly of particles as passive vibration damping devices, however, the literature is meager. Thanks mainly to the publications of Dr. Panossian beginning in the late eighties 6,7,8 that the importance of particles as a passive damping media has been brought to the attention of dynamicists. Since then, due to their effectiveness, simplicity and temperature insensitivity, it has attracted the attention of many engineers in industry 9,10,11,12,13 and academia14,15,16,17.

A particle damper consists of a cavity partially filled with a multitude of solid particles. Whereas, a single particle impact damper, also known as acceleration damper, is a special case of a particle damper that has been analyzed extensively in the literature18. The cavity of the particle damper may take many

45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference19 - 22 April 2004, Palm Springs, California

AIAA 2004-1906

Copyright © 2004 by Stepan Simonian. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.

different forms, such as a series of drilled holes 6 into an existing structure that is exposed to vibratory disturbances, or it could be an external container attached to a vibrating structure. Most of the current applications utilize the latter approach using cavities in various shapes and sizes.

Most of the engineering applications of particle dampers focus on experimental techniques to arrive at viable damper designs for their particular application. However, recently three techniques have been utilized to analytically approximate the dynamics of particle assemblies and derive energy dissipation characteristics at various vibration amplitude regimes. Molecular Dynamics (MD) and related numerical technique have been utilized in Refs. 19, 20 and 21. Based on parametric numerical simulations, in a recent study, three regimes have been identified for the rate of energy loss19: namely (a) solid, (b) convective and (c) gas-like states. The gas-like regime, where most of the particles move in unison, appear to be the most promising for practical applications19 yielding high values of energy dissipation capability. A second numerical approach is called Distinct Element Method (DEM) or Discrete Element Method developed in Ref. 22. A number of studies have appeared recently using this numerical approach23, 24,25. Both MD and DEM models determine the behavior of an idealized granular material by calculating the motion of individual particles as they interact with each other and the boundaries. Appropriate space and time averaging schemes determine macroscopic properties. A third analytical modeling method of particle dampers is based on modeling the particles as an “equivalent single mass” impact or acceleration damper26.The analytical theory of the impact damper has been developed in the early sixties. See Ref. 18 for a recent survey of impact dampers. A. Applications to Beam Like Space Structures

Beginning in the late 1994, the author applied particle dampers to damp excessive vibrations of two spacecraft cantilever beam type appendages. During early conceptual design stages, engineering model versions of the appendages were equipped with particle dampers (small rectangular containers partially filled with lead shot) and subjected to “twang” transient free-vibration tests. The results of these early tests were reported in Ref. 10. The main conclusions were that using 15-20% of the effective masses of the appendages the fundamental cantilever modes were damped between 5-20 % of critical damping.

The first appendage had a first resonant mode of 31 Hz and inherent damping of 0.5% of critical. With the particle damper attached near the tip, the damping was raised to 4% of critical in the direction of gravity, and 5% in a direction perpendicular to gravity vector using 0.30 lb mass of lead particles. The second appendage had a fundamental frequency of 21 Hz and inherent damping of 3% of critical. In three separate runs 0.1, 0.2 and 0.3 lb lead particles were used in cavity depths of 0.31,0.5 and 0.68 inch, respectively. The damping measurements for these three cases were 7%, 8% and 13% of critical, respectively. A typical measured acceleration trace near the appendage tip, close to the damper location is depicted in Figure 1; from this acceleration trace three damping regimes are identified. A high damping, a medium damping and low damping regions, depicted by I, II and III, respectively. Region I, at the beginning of the twang, has the highest damping factor and is caused predominantly by momentum transfer and inelastic collision effects. Here, the damper cavity top and bottom or sidewalls impact the particles transferring momentum to the particles, this has a “breaking effect” on the cavity. Similar behavior is also observed in single particle impact dampers. In region II, immediately following region I, the measured damping is typically lower than the first region. It is postulated that the damping here is due mostly to dry friction between particles and particle/cavity interfaces. As for region III, immediately following region II, it has the least amount of damping. In this region the particles are at rest in the cavity, the damping is due to primarily to inherent damping originating at beam joints, and due to material damping effects within the beam body.

The same appendages were also subjected to forced vibration sine sweep tests. The forced vibration tests using electrodynamic shakers simulate better the forced vibration flight environment during spacecraft launch events. For these tests, each of the appendages were exposed to two different types of dynamic environments: a sine sweep vibration test, followed by three-axes random vibration tests. The purpose of the sine sweeps was to characterize the damping properties, whereas the purpose of the random vibration was to demonstrate the ability to survive exposure to the environment. After the random test, an abbreviated sine sweep test was performed on each unit to assess any potential changes to the damping performance.

The minimum appendage damping requirements are provided in Table 1. The post-random sine sweep vibration damping characteristics of each of the particle dampers tested are presented in Table 2. As can be seen from this table, in all cases the measured performance exceeded the requirements by +4.3 to + 123%. These values all correspond to an amplitude of approximately 12 g peak response acceleration, as measured close to the effective mass center of the boom-bending mode. The 12 g acceleration amplitude was selected as the desired limiting value for response in the flight environment, and therefore the critical amplitude for assessing damper performance. Measurements were also made at lower amplitude levels; the variation in damping performance with respect to amplitude is shown in Figures 2, 3, 4 and 5. Transmissibility plots with and without particle dampers are depicted in Figures 6 and 7, for the second and first appendage, respectively.

Comparing the measured damping results obtained from free-vibration and the forced vibration tests, the following observations can be made: (a) Higher-damping results in the high amplitude regime (Region I) in the free-vibration application case than during forced vibration. This will also depend on actual amplitudes in each case. (b) Larger gap sizes (between particle top surface and cavity lead) in free-vibrations produce higher damping in the high amplitude vibration region. However, in the forced vibration case, the resulting damping performance depends on vibration amplitude and gap size. There is an optimal gap size, which maximizes damping for a given vibration amplitude. Based on the above observations with different damper behavior during free and forced vibration applications, it is recommended that the particle damper be optimized based on the appropriate application environment.

In a different space instrument application, particle dampers were designed and tested to withstand extremely cold cryogenic temperature environment. The main goal was to protect the delicate instrument from high amplitude vibrations during launch events. For this particular application, common vibration suppression designs using viscoelastic materials or viscous fluids were not design options due to their temperature sensitivity. For polymer and fluid materials, temperature sensitivity of the elastic modulus and damping will alter the dynamic characteristics of the instrument during on orbit operations. Thus, a particle damper was selected for their excellent performance under high amplitude vibrations and insensitivity to extreme temperature variations. This particular device had a beam like structure and had a resonant frequency of 212 Hz with a Q factor of 53. When subjected to the random launch environment, the instrument produced an overall acceleration response amplitude of 25.6 grms . A small cavity box with inside dimensions 0.50x0.61x0.90 inch was designed to contain 30 grams of lead shot. The free air gap for this cavity was 0.005 inch. The damper was attached near the beams effective mass center that would experience the maximum deflection during flight. The device was exposed to various random vibration input levels and damping performance evaluated using half power bandwidth method as well as the amplitude of the transfer function. The damping Q factor is depicted in Figure 8. As can be seen from this plot the Q factor varies from approximately 2.2 to 12 at various input amplitudes. Due to its design simplicity and effective performance, particle dampers are now a standard feature for these devices. A plot which displays the transmissibility of this device at 0 dB level (input of 9.1 grms) with and without the damper is depicted in Figure 9. B. Automotive Applications Particle damper designs were also successfully applied to suppress steering wheel vibrations during idling, and to suppress noise and vibration of electric motors used in steering control systems in the automotive industry.

A steering wheel particle damper is designed to replace a much more expensive elastomeric tuned-mass damper. The motor particle damper is specially designed to suppress a high frequency torsional vibration mode of the motor that is responsible for generating an annoying noise level. This particular damper design for the motor is composed of an annular circular cavity with internal pie-shaped radial partition walls to make the damper effective during torsional oscillations of the motor spigot to which it is mounted. Sample test results are shown in Figures 10 and 11 for the steering wheel simulator and motor vibration tests, respectively. As can be seen from these initial test results, the particle dampers are quite effective in reducing vibration amplitudes. A patent has been applied and is pending for the above mentioned applications 27.

C. Ball-in-Cavity Particle Damper One of the limiting factors for the performance of particle and impact dampers have been their

unsatisfactory behavior under low amplitude vibrations in a one g environment 9. This is especially true for damper lateral vibration performance. Based on extensive tests on various particle damper design configurations Ref. 9 concludes that for lateral vibrations the dampers are not effective below 0.3 g acceleration level, due to the presence of static dry friction between the particles and the container floor, unless the particles are suspended in a bag, like a pendulum. However, a pendulum-like arrangement may not be practical for a number of applications due to geometric design constraints. One way to overcome this low amplitude limitation is to place the particle in a suitable plastic or elastomeric ball. This was done in a simple test towards the end of 1994. A medium hardness thin walled plastic ball was utilized with one-inch diameter. A small hole was drilled on the ball and partially filled with tungsten particles. The total weight of the ball and particles were 42 grams. The ball was placed in a rectangular cavity box with inside lateral dimensions of 1.25 inches and a vertical height of 1.6 inch. The damper was attached at the end of a 24 Hz cantilever beam and vibrated with the shaker in the direction of gravity and at an angle perpendicular to the gravity vector (lateral direction). The beam without a damper had a Q of 55. With the damper attached and a 3 g input sine sweep in the direction of gravity, a Q value of slightly less than 6 was measured (see Figure 12). Clearly, this ball-in-cavity particle damper solves the problem mentioned in Ref. 9 since the ball will roll laterally within the cavity for lateral accelerations much below 0.3 g. This device resembles a single mass impact damper but with the added advantage of better performance compared with the regular impact damper. This device eliminates much of the noise of the former, possesses inter-particle dry friction mechanism, in addition to momentum exchange and non-elastic impact losses as well as lower amplitude operating capability. There were no attempts to further optimize the damper capability since the resulting performance was already excellent.

D. Tubular Particle Beam Damper

A very different class of particle damper is depicted in Figure 13. Here the particles are filled in a resilient elastomeric or plastic tube. As more and more particles are forced into the resilient tube, the tube stretches diametrically to accommodate the added particles. Thus, depending on the tube nominal diameter and the amount of particles forced into the tube, it is possible to vary the inter-particle contact forces by the preload provided by the diametrically and longitudinally stretched tube. Other flexible metallic tubes can also be substituted instead of the polymeric tubes with similar effects. The particle filled tube can now be used as a cantilevered impact damper. This can be accomplished by attaching this beam in a tubular cavity fixed on a vibrating member. Depending on the magnitude of inter-particle contact forces induced by the elasticity of the stretched tube, large frictional forces can be generated within the particles if the tube is deformed by the action of vibration imposed on it. In a typical application, the particle tube is mounted in a cavity in a horizontal cantilevered configuration. A desired gap size separates the free end of the particle-beam and the cavity wall surrounding it. This device is attached to a vibrating structure to damp its vibration amplitude. The device operates as a combination of impact/friction damper. At high vibration amplitudes, the tip of the particle-beam impacts the cavity walls thus controlling vibration by three mechanisms: momentum transfer, dry friction and non-elastic impact losses in the particles. For lower amplitude vibrations, there are no impact losses within the particle-tube but inter-particle friction dissipates vibration energy. The frictional stick-slip dissipative forces will be acting as long as the vibration amplitude is large enough to deform the particle-tube. A patent has been awarded for this application 28. This device has been shown to be extremely effective to damp ski vibrations in icy downhill snow environments.

The author is currently working on other applications of particle dampers. Also several new particle damper designs are currently under investigation.

As shown above, these simple and inexpensive devices have a wide range of application in diverse disciplines such as aerospace, ground transportation and high performance sporting equipment industry.

E. References

1Melo, F., Umbanhowar, P. B., and Swinney, H. L., “Hexagons, Kinks, and Disorder in Oscillated Granular Layers,” Physical Review Letters, Vol.75, No. 21, 1995, pp. 3838-3841.

2Jaeger, H. M., Nagel, S. R., and Behringer, R. P., “Granular Solids, Liquids, and Gases,” Reviews of Modern Physics, Vol. 68, No. 4, 1996, pp. 1259-1273.

3Wolf, N. D., “Results of Loss Factor Measurements on Steel and Concrete Beams using a Viscoelastic or Sand Damping System,” WPAFB, Tech. Document No.ASD-TDR-62-717, Sept.1962. 4Popplewell, N., and Semercigil, S. E., “Performance of the Bean Bag Damper for a Sinusoidal External Force,” Journal of Sound and Vibration, Vol. 133, No. 2,1989, pp. 193-223. 5Lenzi, A., “The Use of Damping Material in Industrial Machines,” Ph.D. Dissertation, Faculty of Engineering and Applied Science, Univ. of Southamton, Southamton, UK, 1985. 6Panossian, H. V., “Nonobstructive Impact Damping Applications for Cryogenic Environments,” Proceedings of Damping ’89, 1989, pp. KBC 1-9. 7Panossian, H. V., “Nonobstructive Particle Damping: A New Passive Damping Technique,” Shock and Vibration, Vol. 1, No. 6, 1991, pp. 4-10. 8Panossian, H. V., “Structural Damping Enhancement Via Non-Obstructive Particle Damping Technique,” ASME Journal of Vibration and Acoustics, Vol. 114, 1992, pp. 101-105. 9Cempel, C. and Lotz, G., “ Efficiency of Vibrational Energy Dissipation by Moving Shot,” Journal of Structural Engineering, Vol. 119, No. 9, 1993, pp. 2642-2652.

10Simonian, S. S., “Particle Beam Damper,” Proceedings of SPIE, Smart Structures and Materials: Passive Damping, 2445, 1995, pp. 149-160.

11Martin, M. and Warwick, D., “An Evaluation of Polyethylene Beads as a Damping Treatment for a Lightweight Aluminum Truss,” Navel Surface Warfare Center, Carderock Division, Report CDNSWC-SIG-95-090-7250, July 1995.

12Hollkamp, J. J. and Gordon, R. W., “Experiments with Particle Damping,” Proceedings of SPIE, Smart Structures and Materials: Passive Damping and Isolation, 3327, 1998, pp. 2-12.

13Fricke, R., “Lodengraf Damping- An Advance Vibration Damping Technology,” Sound and Vibration, July 2000, pp. 22-27.

14Papalou, A. and Masri, S. M., “An experimental Study of Particle Dampers Under Random Excitation,” Proceedings of First World Conf. On Structural Control, Los Angeles, California, Aug. 1994, pp. FP2-18 to FP2-24.

15Yokomichi, I., Araki, Y., Jinnouchi, Y. and Inoue, J., “Impact Damper with Granular Materials for Multibody System,” ASME, Journal of Pressure Vessel Technology, Vol. 118, Feb. 1996, pp. 95-103.

16Saeki, M., “Impact Damping with Granular Materials in a Horizontally Vibrating System,” Journal of Sound and Vibration, Vol. 251, No.1, 2002, pp. 153-161.

17Xu, Z., Wang, M. Y. and Chen, T., “An Experimental Study of Particle Damping for Beams and Plates,” ASME, Journal of Vibration and Acoustics, Vol. 126, January 2004, pp. 141-148.

18Ekwaro-Osire, S. and Desen, I. C., “Experimental Study of an Impact Vibration Absorber,” Journal of Vibration Control, Vol. 7, 2001, pp. 475-493.

19Saluena, C., Esipov, S. E., Poschel, T. and Simonian, S., “ Dissipative Properties of Granular Ensembles,” Proceedings of SPIE, Smart Structures and Materials: Passive Damping and Isolation, 3327, 1998, pp. 23-29.

20Saluena, C., Esipov, S. E., Rosenkranz, D. and Panossian, H., “ On Modeling of Arrays of Passive Granular Dampers,” Proceedings of SPIE, Smart Structures and Materials: Passive Damping and Isolation, 3672, 1999, pp. 32-42.

21Olson, S. E., “An analytical Particle Damping Model,” Journal of Sound and Vibration, Vol. 264,2003, pp. 1155-1166.

22Cundall, P. and Strack, O., “A Distinct Element Model for Granular Assemblies,” Geotechnique, Vol. 29, 1979, pp. 47-65.

23Hoffmann, K. H. and Schreiber, M. (Eds.), D.E., Modeling and Computer Simulation of Granular Media, in Computational Physics: Selected Methods-Simple Exercises- Serious Applications, by Wolf, D. E., Heidelberg, Springer, 1996.

24Chen, T., Mao, K. Huang, X. and Wang, M. Y., “Dissipation Mechanism of Non-obstructive Particle Damping Using Discrete Element Method,” Proceedings of SPIE, Smart Structures and Materials: Damping and Isolation, 4331, 2001, pp. 294-301.

25Saeki, M., “An Analytical Model for Multi-Particle Impact Damping,” Proceedings Fifth World Congress on Computational Mechanics,” July, 2002.

26Papalou, A. and Masri, S. M., “Performance of Particle Dampers Under Random Excitation,” ASME, Journal of Vibration and Acoustics, Vol. 118, pp. 614-621.

27Simonian, S. S., Pillsbury, C. S., Braun, W. P. and Parker, A. D., U.S. Patent application for, “ Damping Vibration for a Vehicle Part,” TRW Project No. 010954-00US(IR), Docket No. TRW (AP) 5949, June 2002.

28Simonian, S. S., Calif., “Vibration Damping Devices for Skis and Other Applications,” U.S. Patent No. 5678840, 1997.

Table 1: Damper Performance Requirements (Damping Factor of Critical)

Table 2: Measured Particle Damper Performance (%)

Unit Axis Requirement (%) Capability (%) Capability (%) Unit 1 Unit 2

Appendage 1 Z 4 6.0 4.2 Appendage 1 Lateral 4 8.9 7.8

Unit 1 Unit 3 Appendage 2 Z 7 7.3 7.3 Appendage 2 Lateral 2 4.9 5.1

.

Unit Axis

Damping (%)

Appendage 1 Z 4 Appendage 1 Lateral 4 Appendage 2 Z 7 Appendage 2 Lateral 2

Figure 1: Transient Response of Beam With Particle Damper

Figure 2: Appendage 1, Finite Element Response Predictions versus Damping

Figure 3: Appendage 1, Measured Damping versus Amplitude: Gap Size Effects

Figure 4: Appendage 1, Measured Damping versus Amplitude: Shot Weight Effects

Figure 5: Appendage 2, Measured Damping versus Amplitude

Figure 6: Appendage 2, With and Without Particle Damper

Figure 7: Appendage 1, With and Without Particle Damper

Figure 8: Measured Damping versus Input Amplitude

Figure 9(a): Transmissibility Without Particle Damper

Figure 9(b): Transmissibility With Particle Damper

Figure 10(a): Torsional/Bending Motor Particle Damper

Figure 10(b): Measured Lateral Response: Torsional/Bending Motor Particle Damper

Figure 11(a): Mass Simulated Steering Wheel Sine Sweep Vibration Test Results: With and Without Particle Damper

Figure 11(b): Mass Simulated Steering Wheel, Sine Sweep Vibration Test Setup: (Damper not shown)

0

10

20

30

40

50

60

70

80

20 25 30 35 40 45 50

Q versus Resonant Frequency Measurements Shaker input = 0.3 g

Steering Wheel simulator Effective mass = 8.8 lb (VW Jetta)

Q (gap=3.7mm)Q (gap=6.2mm)Q (gap=8.7mm) Q (no Damper)

Figure 12: Measured Transmissibility of Beam With Ball-in-Cavity Particle Damper (Q = 55 Without Damper)

Figure 13(a): Tubular Particle Beam Damper

Figure 13(b): Tubular Particle Beam Damper Applied to Ski Tip (US Patent No. 5,678,840)