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Performance of a New Fine Particle Impact Damper

Performance of a New Fine Particle Impact Damper Hindawi Publishing Corporation Advances in Acoustics and Vibration Volume 2008, Article ID 140894, 6 pages doi:10.1155/2008/140894 Research Article 1, 2 2 2 2 2 Yanchen Du, Shulin Wang, Yan Zhu, Laiqiang Li, and Guangqiang Han College of Medical Instrumentation and Food Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China College of Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China Correspondence should be addressed to Yanchen Du, duyanchen@hotmail.com Received 7 April 2008; Revised 15 July 2008; Accepted 28 July 2008 Recommended by Mohammad Tawfik The energy dissipation mechanisms of conventional impact damper (CID) are mainly momentum exchange and friction. During the impact process, a lot of vibration energy cannot be exhausted but reverberated among the vibration partners. Besides, the CID may produce the additional vibration to the system or even amplify the response in the low-frequency vibration. To overcome these shortcomings, this paper proposes a new fine particle impact damper (FPID) which for the first time introduces the fine particle plastic deformation as an irreversible energy sink. Then, the experiments of the cantilevered beam with the CID and that with the FPID are, respectively, carried out to investigate the behavior of FPID. The experimental results indicate that the FPID has a better performance in vibration damping than in the CID and the FPID works well in control of the vibration with frequency lower than 50 Hz, which is absent to the non-obstructive particle damper. Thus, the FPID has a bright and significant application future because most of the mechanical vibration falls in the range of low freqency. Copyright © 2008 Yanchen Du et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION deformation of bumpers to absorb energy from collisions, so that the losses in the accidents could be alleviated [15]. Wang [16] found that plastic deformation as an irre- Impact damping technology has been developed and widely versible energy sink is prone to occur in the plastic or used for decades in manufacture of machine tool, robot, fine particles, especially under the circumstance of violent turbo machine, airplane, rocket launcher, and so forth. At vibration. Based on these findings, in this paper, we propose present, representative conventional impact damper (CID) a new fine particle impact damper (FPID) which for the first includes single unit impact damper [1–5], multiunit impact time introduces the plastic deformation in fine particles to damper [6–8], bean bag impact damper [9, 10], and non- vibration system as perpetual energy dissipation. obstructive particle damper [11, 12]. Any one of CID features momentum exchange or friction, where momentum exchange cannot exhaust vibration energy but reverberates it 2. STRUCTURE AND MECHANISM OF FPID among impact partners [1–5], andfrictionisonlygood at the high-frequency vibration but bad or even magnifying at Fine particles are enrolled as damping agents among the the low-frequency vibration [12]. impact partners (larger balls as usual) in FPID, as shown It is well known that plastic deformation can exhaust in Figure 1. Because the surface attraction of fine particles energy as an irreversible energy sink. Many efforts have been is greater than its gravity [17], the whole surface of impact made to use plastic deformation to absorb shock and vibra- partners is surrounded and affixed by the fine particles. tion energy such as civil engineers utilize plastic deformation The FPID, in which the plastic deformation of fine particles of minor structures to absorb earthquake energy, so that due to collisions of impact partners exhausts most of the the damage could be limited, and the major structure may vibration energy, for the first time introduces the plastic be kept safe [13]; ship engineers utilize plastic deformation deformation of fine particles as perpetual energy dissipation of ship bow to absorb collision energy between ship and and overcomes the shortcomings of momentum exchange pier, so that both the ship and the pier could be prevented and friction. Thus, it is necessary to investigate the perfor- from damage [14]; automobile technicians utilize plastic manceofFPIDbyexperiments. 2 Advances in Acoustics and Vibration Force hammer Accelerometer 1 2 3 4 5 6 7 8 9 10 11 DLF dual DASP2003 INV data channel acquisition signal amplifier system analyzer Figure 3: Schematic diagram of experimental scheme for mode Figure 1: Structure of FPID. analysis. Accelerometer Damper beam, damped by the FPID with different volumetric Function Power packing ratio r of 100 µm in diameter copper particles, are generator amplifier Dual channel amplifier measured at harmonic excitation. For the filled 100 µmin diameter copper particles in the FPID designed in this paper, Electromagnetic Data acquisition system the relation between volumetric packing ratio r and mass m exciter is listed in Table 2. The experiments of cantilevered beam, damped by the Signal analyzer FPID with r = 20% of 100 µm in diameter copper particles and that with r = 20% of 400 µm in diameter zinc particles, Figure 2: Schematic diagram of experimental setup. are performed at harmonic excitation to indicate the effect of different mental particles. 3. EXPERIMENTAL DESCRIPTIONS 4. MODE ANALYSIS ON CANTILEVERED BEAM We use a damped cantilevered beam as depicted in Figure 2 in these experiments. The cantilevered beam made of steel is The mode analysis on the undamped cantilevered beam 315 mm in length, 45 mm in width, and 2.1 mm in thickness. adopts the signal analysis system manufactured by the China The damper container is fixed near the tip of cantilevered Orient Institute of Noise and Vibration. The cantilevered beam, where the largest displacement is obtained at the first beam tested is equally divided into ten parts, and an flexural mode of 12.9 Hz. The damper container is in the accelerometer is placed on the fifth point to measure the shape of column with 12 mm in diameter and 20 mm in response. A force hammer knocks each point five times and height, also made of steel. In the damper container, a 10 mm for each knocking, the force signal from the force hammer in diameter steel ball with 4.1 g mass and a small quantity and the acceleration signal measured on the fifth point are of copper particles with 100 µm in diameter are filled. The collected by the data acquisition system. The mode analysis accelerometer placed on the back of the damper measures the based on these signals is performed with the signal analysis tip displacement of the beam which is excited near the root software. The experimental scheme for the mode analysis is through a stinger attached to an electromagnetic exciter. shown in Figure 3. To investigate the performance of FPID, experiments The obtained top five flexural modes of cantilevered are, respectively, carried out on the undamped beam, on beam are shown in Figure 4. the beam damped by particle impact damper, on the beam damped by single unit impact damper, and on the beam 5. EXPERIMENTAL RESULTS damped by FPID. The contents of damper cavity in above four cases are listed in Table 1. In these four cases, the tip Figure 5 shows the experimental results under free vibration displacement of cantilevered beam at free vibration and with the same initial displacement from the four cases that for the first flexible mode at harmonic excitation are listed in Table 1. The particle impact damper including measured to study the performance of FPID. 4.6 g copper particles in the cavity has only a little effect In the FPID, the damper cavity is filled with the fine on the reduction of the tip displacement of cantilevered particles and a steel ball with 10 mm in diameter. As shown beam; the single unit impact damper even magnifies the in Figure 1, assume that the damper cavity has a total volume tip displacement for the violet collision between steel and of V , the steel ball has a volume of V , and the filled fine c b cavity; the FPID of r = 20% of copper particles has a good particles have a volume of V . Thus, we define the fine performance in the rapid attenuation of the tip displacement. particles volumetric packing ratio r in the FPID as Figure 6 shows the experimental results under the same harmonic excitation from the four cases listed in Table 1.The r = . (1) p particle impact damper only including 4.6 g copper particles V − V c b in the cavity makes the tip displacement of cantilevered To test the effect of quantity of filled fine particles on the beam reduce approximately 20% for the first flexural mode; performance of FPID, the tip displacements of cantilevered the single unit impact damper has the similar performance Yanchen Du et al. 3 (a) (b) (c) (d) (e) Figure 4: Schematic diagram of the top five flexural modes of cantilevered beam (a) the first flexural mode (13.183 Hz), (b) the second flexural mode (89.889 Hz), (c) the third flexural mode (262.667 Hz), (d) the fourth flexural mode (448.979 Hz), (e) the fifth flexural mode (524.518 Hz). 50 50 40 40 30 30 20 20 10 10 0 0 −10 −10 −20 −20 −30 −30 −40 −40 −50 −50 01 2 3 4 5 6 01 2 3 4 5 6 Time (s) Time (s) (a) (b) 50 50 40 40 20 20 10 10 0 0 −10 −10 −20 −20 −30 −30 −40 −40 −50 −50 01 2 3 4 5 6 01 2 3 4 5 6 Time (s) Time (s) (c) (d) Figure 5: Tip displacement histories of the cantilevered beam with (a) no damper, (b) particle impact damper, (c) single unit impact damper and (d) FPID with r = 20% of copper particles, at free vibration of the same initial displacement. Displacement (mm) Displacement (mm) Displacement (mm) Displacement (mm) 4 Advances in Acoustics and Vibration Table 1: Contents in damper cavity. Case Damper type Steel ball in damper cavity Copper particles in damper cavity (1) No damper None None (2) Particle impact damper None 100 µm in diameter, 4.6 g mass (3) Single unit impact damper Single, 10 mm in diameter, 4.1 g mass None (4) FPID Single, 10 mm in diameter, 4.1 g mass 100 µm in diameter, 0.5 g mass Table 2: Relation between volumetric packing ratio r and mass m for the filled copper particles in the FPID. Volumetric packing ratio r 10% 20% 40% 60% 80% 100% Mass m (g) 0.25g 0.5g 1.0g 1.5g 2.0g 2.5g 11 12 13 14 15 0 11 12 13 14 15 Frequency (Hz) Frequency (Hz) Figure 6: Tip displacement of the cantilevered beam with no Figure 7: Tip displacement of the cantilevered beam with single damper (), particle impact damper (), single unit impact unit impact damper (), FPID with r = 10% of copper particles damper (♦) and FPID with r = 20% of copper particles (), at (), FPID with r = 20% of copper particles (), FPID with the same harmonic excitation. r = 40% of copper particles (), FPID with r = 60% of copper p p particles (♦)and FPID with r = 80% of copper particles (), at the same harmonic excitation. as the particle impact damper; the FPID of r = 20% of copper particles is good at damping, which makes the tip displacement of cantilevered beam reduce over 65% for the The results show that there exists an optimal packing first flexural mode. ratio of particles in FPID, which is similar to the particle These results show that the FPID has significant ability impact damping. When the packing ratio is too large, to absorb vibration energy and works well in low frequency the impact partner does not have enough space to be (lower than 50 Hz). Because the auxiliary masses are kept excited, which limits the plastic deformation occurred in same in the last three cases (particle impact damper, single fine particles. While when the packing ratio is too little, the unit impact damper, and FPID with r = 20% of copper impact partner is not coated sufficiently, and thus the FPID particles), the excellent performance of FPID can be only behaves more like a single unit impact damper. attributed to the plastic deformation occured in the fine The FPID of r = 20% of 100 µm in diameter copper particles. particles and that of r = 20% of 400 µm in diameter zinc Figure 7 is the experimental results from the FPID with particles are compared at the same harmonic excitation, as different volumetric packing ratio r of 100 µm in diameter shown in Figure 8.The FPID of r = 20% of 100 µmin p p copper particles at the same harmonic excitation. The FPID diameter copper particles is only a little better than that of of r = 20% and that of r = 40% work better than others, r = 20% of 400 µm in diameter zinc particles, especially at p p p that is, too little or too much volumetric packing ratio r has the the first resonant point. It seems that both the material bad effect on the performance of FPID. No matter how much and the geometrical sizes of the fine particles (especially copper particles are, the FPID has better damping ability metal particles) do not alter the performance of FPID. While than the single unit impact damper. the samples used in this paper are still very limited, thus the Displacement (mm) Displacement (mm) Yanchen Du et al. 5 significantly different response than a single particle with equivalent plastic deformations because the lower coefficient of restitution usually would not happen in the conventional impact damper. ACKNOWLEDGMENT The authors would like to thank the support from the National Natural Science Foundation of China (Grant no. 50375100). REFERENCES [1] S. F. Masri, “Steady-state response of a multi-degree system 10 11 12 13 14 15 with an impact damper,” Journal of Applied Mechanics, vol. 3, Frequency (Hz) pp. 127–132, 1973. [2] S. F. Masri, “General motion of impact dampers,” The Journal Figure 8: Tip displacement of the cantilevered beam with FPID of the Acoustical Society of America, vol. 47, no. 1B, pp. 229– with r = 20% of copper particles () and FPID with r = 20% of p p 237, 1970. zinc particles (♦), at the same harmonic excitation. [3] S. F. Masri, “Theory of the dynamic vibration neutralizer with motion-limiting stops,” Journal of Applied Mechanics, vol. 7, pp. 563–568, 1972. effect of different material and size scale of fine particles on [4] C. N. Bapat and S. Sankar, “Single unit impact damper in free the performance of FPID deserves further research. and forced vibration,” Journal of Sound and Vibration, vol. 99, no. 1, pp. 85–94, 1985. 6. CONCLUSIONS [5] L. A. Chen and S. E. Semercigil, “A beam-like damper for attenuating transient vibrations of light structures,” Journal of This paper proposes the FPID which introduces the fine Sound and Vibration, vol. 164, no. 1, pp. 53–65, 1993. particles plastic deformation as an irreversible energy sink. [6] C. N. Bapat and S. Sankar, “Multiunit impact damper—re- From the experiments of the cantilevered beam damped by examined,” Journal of Sound and Vibration, vol. 103, no. 4, pp. the FPID and that by the CID, we draw the conclusions as 457–469, 1985. follows. [7] S. Wang and Y. Du, “Control and application of impact chaos,” in Proceedings of the Asia-Pacific Vibration Conference, vol. 3, (1) The FPID has a better performance than the CID pp. 999–1001, Jilin Science and Technology Press, Hangzhou, in the rapid attenuation of the tip displacement of China, October 2001. cantilevered beam at the free vibration. [8] S. Wang, “Impact chaos control and stress release—a key for development of ultra fine vibration milling,” Progress in (2) The FPID can make the tip displacement of can- Natural Science, vol. 12, no. 5, pp. 336–341, 2002. tilevered beam reduces over 65% for the first flexural [9] N. Popplewell and S. E. Semercigil, “Performance of the bean mode at the harmonic excitation, which is much bag impact damper for a sinusoidal external force,” Journal of more excellent than that of the CID. Sound and Vibration, vol. 133, no. 2, pp. 193–223, 1989. (3) There exists an optimal volumetric packing ratio to [10] C. Cempel andG.Lotz, “Efficiency of vibrational energy achieve the better performance of FPID; no matter dissipation by moving shot,” Journal of Structural Engineering, how much particles are, the FPID has better damping vol. 119, no. 9, pp. 2642–2652, 1993. ability than the single unit impact damper. [11] H. V. Panossian, “Structural damping enhancement via non- obstructive particle damping technique,” Journal of Vibration (4) The mental particles of the same volumetric packing and Acoustics, vol. 114, no. 1, pp. 101–105, 1992. ratio have only a little influence on the performance [12] Z. Xu, M. Y. Wang, and T. Chen, “Particle damping for passive of FPID at the harmonic excitation, and the effect of vibration suppression: numerical modelling and experimental different material and size scale of fine particles on investigation,” JournalofSound andVibration, vol. 279, no. 3– the performance of FPID deserves further research. 5, pp. 1097–1120, 2005. (5) The FPID works well in the frequency lower than [13] A. Wei and L. Ai, “Design and study of coupling beam 50 Hz, which is absent in the non-obstructive particle in seismic resistant RC shearwall structure,” Architecture damper. Technology, vol. 37, no. 2, pp. 140–141, 2006. [14] J.-C. Liu and Y.-N. Gu, “Mechanism of plastic protection In spite of so many conclusions are drawn from this device for ship-bridge collision,” Journal of Shanghai Jiaotong paper, the study has not compared the performance of University, vol. 37, no. 7, pp. 990–994, 2003. proposed version to an equivalent conventional impact [15] X. Tan, W. Feng, and H. Zhao, “Finite element method damper having a lower coefficient of restitution to see in impact analysis of automobile’s bumper,” Mechanics and if the plastic deformations of the fine particles cause a Engineering, vol. 26, no. 2, pp. 35–38, 2004. Displacement (mm) 6 Advances in Acoustics and Vibration [16] S. Wang, “Research progress in vibro-particuology,” Mining & Processing Equipment, vol. 30, no. 6, pp. 48–49, 2002. [17] H. Lu, Introduction to Powder Technology, Tongji University Press, Shanghai, China, 1998. 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Performance of a New Fine Particle Impact Damper

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Copyright © 2008 Yanchen Du et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Hindawi Publishing Corporation Advances in Acoustics and Vibration Volume 2008, Article ID 140894, 6 pages doi:10.1155/2008/140894 Research Article 1, 2 2 2 2 2 Yanchen Du, Shulin Wang, Yan Zhu, Laiqiang Li, and Guangqiang Han College of Medical Instrumentation and Food Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China College of Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China Correspondence should be addressed to Yanchen Du, duyanchen@hotmail.com Received 7 April 2008; Revised 15 July 2008; Accepted 28 July 2008 Recommended by Mohammad Tawfik The energy dissipation mechanisms of conventional impact damper (CID) are mainly momentum exchange and friction. During the impact process, a lot of vibration energy cannot be exhausted but reverberated among the vibration partners. Besides, the CID may produce the additional vibration to the system or even amplify the response in the low-frequency vibration. To overcome these shortcomings, this paper proposes a new fine particle impact damper (FPID) which for the first time introduces the fine particle plastic deformation as an irreversible energy sink. Then, the experiments of the cantilevered beam with the CID and that with the FPID are, respectively, carried out to investigate the behavior of FPID. The experimental results indicate that the FPID has a better performance in vibration damping than in the CID and the FPID works well in control of the vibration with frequency lower than 50 Hz, which is absent to the non-obstructive particle damper. Thus, the FPID has a bright and significant application future because most of the mechanical vibration falls in the range of low freqency. Copyright © 2008 Yanchen Du et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. INTRODUCTION deformation of bumpers to absorb energy from collisions, so that the losses in the accidents could be alleviated [15]. Wang [16] found that plastic deformation as an irre- Impact damping technology has been developed and widely versible energy sink is prone to occur in the plastic or used for decades in manufacture of machine tool, robot, fine particles, especially under the circumstance of violent turbo machine, airplane, rocket launcher, and so forth. At vibration. Based on these findings, in this paper, we propose present, representative conventional impact damper (CID) a new fine particle impact damper (FPID) which for the first includes single unit impact damper [1–5], multiunit impact time introduces the plastic deformation in fine particles to damper [6–8], bean bag impact damper [9, 10], and non- vibration system as perpetual energy dissipation. obstructive particle damper [11, 12]. Any one of CID features momentum exchange or friction, where momentum exchange cannot exhaust vibration energy but reverberates it 2. STRUCTURE AND MECHANISM OF FPID among impact partners [1–5], andfrictionisonlygood at the high-frequency vibration but bad or even magnifying at Fine particles are enrolled as damping agents among the the low-frequency vibration [12]. impact partners (larger balls as usual) in FPID, as shown It is well known that plastic deformation can exhaust in Figure 1. Because the surface attraction of fine particles energy as an irreversible energy sink. Many efforts have been is greater than its gravity [17], the whole surface of impact made to use plastic deformation to absorb shock and vibra- partners is surrounded and affixed by the fine particles. tion energy such as civil engineers utilize plastic deformation The FPID, in which the plastic deformation of fine particles of minor structures to absorb earthquake energy, so that due to collisions of impact partners exhausts most of the the damage could be limited, and the major structure may vibration energy, for the first time introduces the plastic be kept safe [13]; ship engineers utilize plastic deformation deformation of fine particles as perpetual energy dissipation of ship bow to absorb collision energy between ship and and overcomes the shortcomings of momentum exchange pier, so that both the ship and the pier could be prevented and friction. Thus, it is necessary to investigate the perfor- from damage [14]; automobile technicians utilize plastic manceofFPIDbyexperiments. 2 Advances in Acoustics and Vibration Force hammer Accelerometer 1 2 3 4 5 6 7 8 9 10 11 DLF dual DASP2003 INV data channel acquisition signal amplifier system analyzer Figure 3: Schematic diagram of experimental scheme for mode Figure 1: Structure of FPID. analysis. Accelerometer Damper beam, damped by the FPID with different volumetric Function Power packing ratio r of 100 µm in diameter copper particles, are generator amplifier Dual channel amplifier measured at harmonic excitation. For the filled 100 µmin diameter copper particles in the FPID designed in this paper, Electromagnetic Data acquisition system the relation between volumetric packing ratio r and mass m exciter is listed in Table 2. The experiments of cantilevered beam, damped by the Signal analyzer FPID with r = 20% of 100 µm in diameter copper particles and that with r = 20% of 400 µm in diameter zinc particles, Figure 2: Schematic diagram of experimental setup. are performed at harmonic excitation to indicate the effect of different mental particles. 3. EXPERIMENTAL DESCRIPTIONS 4. MODE ANALYSIS ON CANTILEVERED BEAM We use a damped cantilevered beam as depicted in Figure 2 in these experiments. The cantilevered beam made of steel is The mode analysis on the undamped cantilevered beam 315 mm in length, 45 mm in width, and 2.1 mm in thickness. adopts the signal analysis system manufactured by the China The damper container is fixed near the tip of cantilevered Orient Institute of Noise and Vibration. The cantilevered beam, where the largest displacement is obtained at the first beam tested is equally divided into ten parts, and an flexural mode of 12.9 Hz. The damper container is in the accelerometer is placed on the fifth point to measure the shape of column with 12 mm in diameter and 20 mm in response. A force hammer knocks each point five times and height, also made of steel. In the damper container, a 10 mm for each knocking, the force signal from the force hammer in diameter steel ball with 4.1 g mass and a small quantity and the acceleration signal measured on the fifth point are of copper particles with 100 µm in diameter are filled. The collected by the data acquisition system. The mode analysis accelerometer placed on the back of the damper measures the based on these signals is performed with the signal analysis tip displacement of the beam which is excited near the root software. The experimental scheme for the mode analysis is through a stinger attached to an electromagnetic exciter. shown in Figure 3. To investigate the performance of FPID, experiments The obtained top five flexural modes of cantilevered are, respectively, carried out on the undamped beam, on beam are shown in Figure 4. the beam damped by particle impact damper, on the beam damped by single unit impact damper, and on the beam 5. EXPERIMENTAL RESULTS damped by FPID. The contents of damper cavity in above four cases are listed in Table 1. In these four cases, the tip Figure 5 shows the experimental results under free vibration displacement of cantilevered beam at free vibration and with the same initial displacement from the four cases that for the first flexible mode at harmonic excitation are listed in Table 1. The particle impact damper including measured to study the performance of FPID. 4.6 g copper particles in the cavity has only a little effect In the FPID, the damper cavity is filled with the fine on the reduction of the tip displacement of cantilevered particles and a steel ball with 10 mm in diameter. As shown beam; the single unit impact damper even magnifies the in Figure 1, assume that the damper cavity has a total volume tip displacement for the violet collision between steel and of V , the steel ball has a volume of V , and the filled fine c b cavity; the FPID of r = 20% of copper particles has a good particles have a volume of V . Thus, we define the fine performance in the rapid attenuation of the tip displacement. particles volumetric packing ratio r in the FPID as Figure 6 shows the experimental results under the same harmonic excitation from the four cases listed in Table 1.The r = . (1) p particle impact damper only including 4.6 g copper particles V − V c b in the cavity makes the tip displacement of cantilevered To test the effect of quantity of filled fine particles on the beam reduce approximately 20% for the first flexural mode; performance of FPID, the tip displacements of cantilevered the single unit impact damper has the similar performance Yanchen Du et al. 3 (a) (b) (c) (d) (e) Figure 4: Schematic diagram of the top five flexural modes of cantilevered beam (a) the first flexural mode (13.183 Hz), (b) the second flexural mode (89.889 Hz), (c) the third flexural mode (262.667 Hz), (d) the fourth flexural mode (448.979 Hz), (e) the fifth flexural mode (524.518 Hz). 50 50 40 40 30 30 20 20 10 10 0 0 −10 −10 −20 −20 −30 −30 −40 −40 −50 −50 01 2 3 4 5 6 01 2 3 4 5 6 Time (s) Time (s) (a) (b) 50 50 40 40 20 20 10 10 0 0 −10 −10 −20 −20 −30 −30 −40 −40 −50 −50 01 2 3 4 5 6 01 2 3 4 5 6 Time (s) Time (s) (c) (d) Figure 5: Tip displacement histories of the cantilevered beam with (a) no damper, (b) particle impact damper, (c) single unit impact damper and (d) FPID with r = 20% of copper particles, at free vibration of the same initial displacement. Displacement (mm) Displacement (mm) Displacement (mm) Displacement (mm) 4 Advances in Acoustics and Vibration Table 1: Contents in damper cavity. Case Damper type Steel ball in damper cavity Copper particles in damper cavity (1) No damper None None (2) Particle impact damper None 100 µm in diameter, 4.6 g mass (3) Single unit impact damper Single, 10 mm in diameter, 4.1 g mass None (4) FPID Single, 10 mm in diameter, 4.1 g mass 100 µm in diameter, 0.5 g mass Table 2: Relation between volumetric packing ratio r and mass m for the filled copper particles in the FPID. Volumetric packing ratio r 10% 20% 40% 60% 80% 100% Mass m (g) 0.25g 0.5g 1.0g 1.5g 2.0g 2.5g 11 12 13 14 15 0 11 12 13 14 15 Frequency (Hz) Frequency (Hz) Figure 6: Tip displacement of the cantilevered beam with no Figure 7: Tip displacement of the cantilevered beam with single damper (), particle impact damper (), single unit impact unit impact damper (), FPID with r = 10% of copper particles damper (♦) and FPID with r = 20% of copper particles (), at (), FPID with r = 20% of copper particles (), FPID with the same harmonic excitation. r = 40% of copper particles (), FPID with r = 60% of copper p p particles (♦)and FPID with r = 80% of copper particles (), at the same harmonic excitation. as the particle impact damper; the FPID of r = 20% of copper particles is good at damping, which makes the tip displacement of cantilevered beam reduce over 65% for the The results show that there exists an optimal packing first flexural mode. ratio of particles in FPID, which is similar to the particle These results show that the FPID has significant ability impact damping. When the packing ratio is too large, to absorb vibration energy and works well in low frequency the impact partner does not have enough space to be (lower than 50 Hz). Because the auxiliary masses are kept excited, which limits the plastic deformation occurred in same in the last three cases (particle impact damper, single fine particles. While when the packing ratio is too little, the unit impact damper, and FPID with r = 20% of copper impact partner is not coated sufficiently, and thus the FPID particles), the excellent performance of FPID can be only behaves more like a single unit impact damper. attributed to the plastic deformation occured in the fine The FPID of r = 20% of 100 µm in diameter copper particles. particles and that of r = 20% of 400 µm in diameter zinc Figure 7 is the experimental results from the FPID with particles are compared at the same harmonic excitation, as different volumetric packing ratio r of 100 µm in diameter shown in Figure 8.The FPID of r = 20% of 100 µmin p p copper particles at the same harmonic excitation. The FPID diameter copper particles is only a little better than that of of r = 20% and that of r = 40% work better than others, r = 20% of 400 µm in diameter zinc particles, especially at p p p that is, too little or too much volumetric packing ratio r has the the first resonant point. It seems that both the material bad effect on the performance of FPID. No matter how much and the geometrical sizes of the fine particles (especially copper particles are, the FPID has better damping ability metal particles) do not alter the performance of FPID. While than the single unit impact damper. the samples used in this paper are still very limited, thus the Displacement (mm) Displacement (mm) Yanchen Du et al. 5 significantly different response than a single particle with equivalent plastic deformations because the lower coefficient of restitution usually would not happen in the conventional impact damper. ACKNOWLEDGMENT The authors would like to thank the support from the National Natural Science Foundation of China (Grant no. 50375100). REFERENCES [1] S. F. Masri, “Steady-state response of a multi-degree system 10 11 12 13 14 15 with an impact damper,” Journal of Applied Mechanics, vol. 3, Frequency (Hz) pp. 127–132, 1973. [2] S. F. Masri, “General motion of impact dampers,” The Journal Figure 8: Tip displacement of the cantilevered beam with FPID of the Acoustical Society of America, vol. 47, no. 1B, pp. 229– with r = 20% of copper particles () and FPID with r = 20% of p p 237, 1970. zinc particles (♦), at the same harmonic excitation. [3] S. F. Masri, “Theory of the dynamic vibration neutralizer with motion-limiting stops,” Journal of Applied Mechanics, vol. 7, pp. 563–568, 1972. effect of different material and size scale of fine particles on [4] C. N. Bapat and S. 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