Nonlinear vibration in metal plate excited by high-power ultrasonic pulses

Chen Zhao-Jiang; Zhang Shu-Yi; Zheng Kai

doi:10.7498/aps.59.4071

Abstract

Nonlinear vibration phenomena including superharmonics, subharmonics, quasi-subharmonics and chaos in metal plate excited by intensive ultrasonic pulses are studied experimentally and theoretically. In the experiments, the plates are excited by the ultrasonic pulse modulated high frequency vibration, and the nonlinear vibration velocities of the plates are measured by laser vibrometer for different sizes and fixing conditions of the plates. The analysis of time series, frequency spectrum and phase space are also performed to characterize the nonlinear vibration of the plate. According to the experimental conditions, a vibro-impact model with nonlinear contact damping is presented to explore the generation mechanism of the complicated nonlinear vibration in the plate. In the dynamic model, the intermittent vibro-impact between the ultrasonic transducer horn and plate are considered as the main source for generating the strongly nonlinear vibration in the plate. The numerical calculation results are in agreement with the observed experimental phenomena.

Keywords:

Authors and contacts

1.
南京大学声学研究所，近代声学教育部重点实验室,南京 210093

References

[1]	［1］Sathyamoorthy M 1987 Appl. Mech. Rev. 40 1553
[2]	［2］Qiu J, Feng Z C 2000 Comput. Struct. 75 491
[3]	［3］Wang D X, Zhang J W, Wu R H 2008 Acta Phys. Sin. 57 6741 2 (in Chinese) ［王旦霞、张建文、吴润衡 2008 57 6741］
[4]	［4］Amabili M 2008 Nonlinear Vibrations and Stability of Shells and 2 Plates (New York: Cambridge University)
[5]	［5］Astashev V K, Babitsky V I 2007 Ultrasonic Processes and Machines: Dynamics, Control and Applications (Berlin: Springer-Verlag)
[6]	［6］Bao X Q, Bar-Cohen Y, Chang Z S, Dolgin B P, Sherrit S, Pal D S, Du S, Peterson T 2003 IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 50 1147
[7]	［7］Song A J, Han L 2007 Acta Phys. Sin. 56 3820 (in Chinese) ［宋爱军、韩雷 2007 56 3820］
[8]	［8］Favro L D, Han X Y, Ouyang Z, Sun G, Sui H, Thomas R L 2000 Rev. Sci. Instrum. 71 2418
[9]	［9］Wiercigroch M, Neilson R D, Player M A 1999 Phys. Lett. A 259 91
[10]	］Han X Y, Zeng Z, Li W, Islam M S, Lu J P, Loggins V, Yitamben E, Favro L D, Newaz G, Thomas R L 2004 J. Appl. Phys. 95 73792
[11]	］Han X Y, Loggins V, Zeng Z, Favro L D, Thomas R L 2004 Appl. Phys. Lett. 85 1332
[12]	］Zheng K, Zhang S Y, Chen Z J, Fan L, Zhang H 2008 Appl. Phys. Lett. 92 221902
[13]	］Babitsky V I, Krupenin V L 2001 Vibrations of Strongly Nonlinear Systems (Berlin: Springer-Verlag)
[14]	］Wiercigroch M, Dekraker B 2000 Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities (Singapore: World Scientific)
[15]	］Zhang Q C, Wang W, He X J 2008 Acta Phys. Sin. 57 5384 (in Chinese) ［张琪昌、王炜、何学军 2008 57 5384］
[16]	］Wang L, Xu W, Li Y 2008 Chin. Phys. B 17 2446
[17]	］Twiefel J, Potthast C, Mracek M, Hemsel T, Sattel T, Wallaschek J 2008 J. Electroceram. 20 209
[18]	］ Lauterborn W, Cramer E 1981 Phys. Rev. Lett. 47 1445
[19]	］Gong Y J, Zhang D, Xi X Y, Gong X F, Liu Z 2007 Acta Phys. Sin. 56 7051 (in Chinese)［龚燕君、章东、郗晓宇、龚秀芬、刘政 2007 56 7051］
[20]	］Wang W J, Lin R M 2003 J. Sound Vib. 259 1
[21]	］Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[22]	］Takens F 1981 Dynamical Systems and Turbulence, Lecture Notes in Mathematics (Berlin: Springer) p366
[23]	］Yang S Q, Jia C Y 2002 Acta Phys. Sin. 51 2452 (in Chinese) ［杨绍清、贾传荧 2002 51 2452］
[24]	］Oh K, Nayfeh A H 1996 Nonlin. Dynam. 11 143
[25]	］Babitsky V I 1998 Theory of Vibro-Impact Systems and Applications (Berlin: Springer)
[26]	］Ibrahim R A 2009 Vibro-Impact Dynamics: Modeling, Mapping and Application (Berlin: Springer-Verlag)
[27]	］Potthast C, Twiefel J, Wallaschek J 2007 J. Sound Vib. 308 405
[28]	］ Marhefka D W, Orin D E 1996 Proceedings of IEEE Inernational Conference on Robotics and Automation (Vol.2) (Minneapolis: IEEE) p1662
[29]	］Von Groll G, Ewins D J 2002 J. Vib. Acoust. 124 350
[30]	］Ganiev M M 2008 Russ. Aeronaut. 51 56
[31]	］Cao Z Y 1989 Vibration Theory of Plates and Shells (Beijing: China Railway Publishing House) p150 (in Chinese) ［曹志远 1989 板壳振动理论 (北京: 中国铁道出版社) 第150页］
[32]	］Holmes P J 1982 J. Sound Vib. 84 173
[33]	］Jiang Z H, Liu X Y, Peng Y J, Li J W 2005 Acta Phys. Sin. 54 5692 (in Chinese) ［姜泽辉、刘新影、彭雅晶、李建伟 2005 54 5692］
[34]	］Luo G W, Me J H, Zhu X F, Zhang J G 2008 Chaos Soliton Fract. 36 1340

Cited By

[1]	［1］Sathyamoorthy M 1987 Appl. Mech. Rev. 40 1553
[2]	［2］Qiu J, Feng Z C 2000 Comput. Struct. 75 491
[3]	［3］Wang D X, Zhang J W, Wu R H 2008 Acta Phys. Sin. 57 6741 2 (in Chinese) ［王旦霞、张建文、吴润衡 2008 57 6741］
[4]	［4］Amabili M 2008 Nonlinear Vibrations and Stability of Shells and 2 Plates (New York: Cambridge University)
[5]	［5］Astashev V K, Babitsky V I 2007 Ultrasonic Processes and Machines: Dynamics, Control and Applications (Berlin: Springer-Verlag)
[6]	［6］Bao X Q, Bar-Cohen Y, Chang Z S, Dolgin B P, Sherrit S, Pal D S, Du S, Peterson T 2003 IEEE Trans. Ultrason. Ferroelectr. Freq. Control. 50 1147
[7]	［7］Song A J, Han L 2007 Acta Phys. Sin. 56 3820 (in Chinese) ［宋爱军、韩雷 2007 56 3820］
[8]	［8］Favro L D, Han X Y, Ouyang Z, Sun G, Sui H, Thomas R L 2000 Rev. Sci. Instrum. 71 2418
[9]	［9］Wiercigroch M, Neilson R D, Player M A 1999 Phys. Lett. A 259 91
[10]	］Han X Y, Zeng Z, Li W, Islam M S, Lu J P, Loggins V, Yitamben E, Favro L D, Newaz G, Thomas R L 2004 J. Appl. Phys. 95 73792
[11]	］Han X Y, Loggins V, Zeng Z, Favro L D, Thomas R L 2004 Appl. Phys. Lett. 85 1332
[12]	］Zheng K, Zhang S Y, Chen Z J, Fan L, Zhang H 2008 Appl. Phys. Lett. 92 221902
[13]	］Babitsky V I, Krupenin V L 2001 Vibrations of Strongly Nonlinear Systems (Berlin: Springer-Verlag)
[14]	］Wiercigroch M, Dekraker B 2000 Applied Nonlinear Dynamics and Chaos of Mechanical Systems with Discontinuities (Singapore: World Scientific)
[15]	］Zhang Q C, Wang W, He X J 2008 Acta Phys. Sin. 57 5384 (in Chinese) ［张琪昌、王炜、何学军 2008 57 5384］
[16]	］Wang L, Xu W, Li Y 2008 Chin. Phys. B 17 2446
[17]	］Twiefel J, Potthast C, Mracek M, Hemsel T, Sattel T, Wallaschek J 2008 J. Electroceram. 20 209
[18]	］ Lauterborn W, Cramer E 1981 Phys. Rev. Lett. 47 1445
[19]	］Gong Y J, Zhang D, Xi X Y, Gong X F, Liu Z 2007 Acta Phys. Sin. 56 7051 (in Chinese)［龚燕君、章东、郗晓宇、龚秀芬、刘政 2007 56 7051］
[20]	］Wang W J, Lin R M 2003 J. Sound Vib. 259 1
[21]	］Packard N H, Crutchfield J P, Farmer J D, Shaw R S 1980 Phys. Rev. Lett. 45 712
[22]	］Takens F 1981 Dynamical Systems and Turbulence, Lecture Notes in Mathematics (Berlin: Springer) p366
[23]	］Yang S Q, Jia C Y 2002 Acta Phys. Sin. 51 2452 (in Chinese) ［杨绍清、贾传荧 2002 51 2452］
[24]	］Oh K, Nayfeh A H 1996 Nonlin. Dynam. 11 143
[25]	］Babitsky V I 1998 Theory of Vibro-Impact Systems and Applications (Berlin: Springer)
[26]	］Ibrahim R A 2009 Vibro-Impact Dynamics: Modeling, Mapping and Application (Berlin: Springer-Verlag)
[27]	］Potthast C, Twiefel J, Wallaschek J 2007 J. Sound Vib. 308 405
[28]	］ Marhefka D W, Orin D E 1996 Proceedings of IEEE Inernational Conference on Robotics and Automation (Vol.2) (Minneapolis: IEEE) p1662
[29]	］Von Groll G, Ewins D J 2002 J. Vib. Acoust. 124 350
[30]	］Ganiev M M 2008 Russ. Aeronaut. 51 56
[31]	］Cao Z Y 1989 Vibration Theory of Plates and Shells (Beijing: China Railway Publishing House) p150 (in Chinese) ［曹志远 1989 板壳振动理论 (北京: 中国铁道出版社) 第150页］
[32]	］Holmes P J 1982 J. Sound Vib. 84 173
[33]	］Jiang Z H, Liu X Y, Peng Y J, Li J W 2005 Acta Phys. Sin. 54 5692 (in Chinese) ［姜泽辉、刘新影、彭雅晶、李建伟 2005 54 5692］
[34]	］Luo G W, Me J H, Zhu X F, Zhang J G 2008 Chaos Soliton Fract. 36 1340

[1]	Zhou Yong. Quantum dynamics study of C—H stretching vibrational excitation in the F+CHD₃ → HF+CD₃ reaction. Acta Physica Sinica, 2024, 73(9): 098201. doi: 10.7498/aps.73.20231832
[2]	Zhao Li-Xia, Wang Cheng-Hui, Mo Run-Yang. Nonlinear acoustic characteristics of multilayer magnetic microbubbles. Acta Physica Sinica, 2021, 70(1): 014301. doi: 10.7498/aps.70.20200973
[3]	Ning Hui, Wang Kai-Cheng, Wang Shao-Meng, Gong Yu-Bin. Vibrational dynamics of hydrogen molecules under intense THz waves. Acta Physica Sinica, 2021, 70(24): 243101. doi: 10.7498/aps.70.20211482
[4]	Shen Huan, Hu Chun-Long, Deng Xu-Lan. Excited-state dynamics of m-dichlorobezene in ultrashort laser pulses. Acta Physica Sinica, 2017, 66(15): 157801. doi: 10.7498/aps.66.157801
[5]	Yu Jie, Guo Xia-Sheng, Tu Juan, Zhang Dong. Mecanism and applications of the nonlinear dynamic response to ultrasound contrast agent microbubbles. Acta Physica Sinica, 2015, 64(9): 094306. doi: 10.7498/aps.64.094306
[6]	Hu Mei, Liu Xin-Guo, Tan Rui-Shan. Influence of collision energy and reagent vibrational excitation on the stereodynamics of reaction Ar+H2+→ArH++H. Acta Physica Sinica, 2014, 63(2): 023402. doi: 10.7498/aps.63.023402
[7]	Ding Hu, Yan Qiao-Yun, Chen Li-Qun. Chaotic dynamics in the forced nonlinear vibration of an axially accelerating viscoelastic beam. Acta Physica Sinica, 2013, 62(20): 200502. doi: 10.7498/aps.62.200502
[8]	Wang Cheng-Hui, Cheng Jian-Chun. Nonlinear forced oscillations of gaseous bubbles in elastic microtubules. Acta Physica Sinica, 2013, 62(11): 114301. doi: 10.7498/aps.62.114301
[9]	Wang Ai-Xing, Liu Yi-Bao, Fang Chao. The study of dynamical potentials of highly excited vibrational states of HOCl. Acta Physica Sinica, 2012, 61(5): 053102. doi: 10.7498/aps.61.053102
[10]	Jin Wei, Wan Zhen-Mao, Liu Yao-Wen. Nonlinear magnetization dynamics excited by the spin-transfer torque effect. Acta Physica Sinica, 2011, 60(1): 017502. doi: 10.7498/aps.60.017502
[11]	Xu Xue-Song, Zhang Wen-Qin, Jin Kun, Yin Shu-Hui. Effect of vibrational quantum number on stereodynamics of reaction O+HCl→OH+Cl. Acta Physica Sinica, 2010, 59(11): 7808-7814. doi: 10.7498/aps.59.7808
[12]	Feng Hai-Ran, Li Peng, Zheng Yu-Jun, Ding Shi-Liang. Dynamical entanglement of vibrations in the linear triatomic molecule by the algebraic approach. Acta Physica Sinica, 2010, 59(8): 5246-5250. doi: 10.7498/aps.59.5246
[13]	Qin Wei-Yang, Yang Yong-Feng, Wang Hong-Jin, Ren Xing-Min. Anticipated synchronization for a class of nonlinear vibration systems. Acta Physica Sinica, 2008, 57(4): 2068-2072. doi: 10.7498/aps.57.2068
[14]	Zhang Qi-Chang, Wang Wei, He Xue-Jun. Homoclinic bifurcation of the strongly nonlinear oscillation system by the normal form method. Acta Physica Sinica, 2008, 57(9): 5384-5389. doi: 10.7498/aps.57.5384
[15]	Song Ai-Jun, Han Lei. Study of nonlinear identification of time series of vibration on transducer in ultrasonic bonding system. Acta Physica Sinica, 2007, 56(7): 3820-3826. doi: 10.7498/aps.56.3820
[16]	Zheng Dun-Sheng, Wu Guo-Zhen. . Acta Physica Sinica, 2002, 51(10): 2229-2232. doi: 10.7498/aps.51.2229
[17]	ZHENG YU-JUN, DING SHI-LIANG. DYNAMICAL SYMMETRY GROUP FOR VIBRATIONAL SPECTRA OF TRIATOMIC MOLECULES. Acta Physica Sinica, 1999, 48(3): 438-445. doi: 10.7498/aps.48.438
[18]	FU ROU-LI, YE HONG-JUAN, FU RONG-TONG, YU ZHI-GANG, SUN XIN. DYNAMICAL STUDY OF NONLINEAR EXCITATION IN FULLERENE C60. Acta Physica Sinica, 1994, 43(8): 1336-1343. doi: 10.7498/aps.43.1336
[19]	XU JI-REN, HUANG NAN-TANG, JIANG YI-FENG, FU GUANG-SHENG, WU ZHEN-QIU. THE STUDY OF VIBRATIONAL ENERGY TRANSFER DYNAMICS IN BCl3 EXCITED BY AN INTENSE INFRARED FIELD. Acta Physica Sinica, 1983, 32(7): 854-866. doi: 10.7498/aps.32.854
[20]	. КВАЗИРЕЛАКСАЦИОННЫЕ КОЛЕБАНИЯ В НЕЛИНЕЙНЫХ ПОСЛЕДОВАТЕЛЬНЫХ ЦЕПЯХ. Acta Physica Sinica, 1965, 21(1): 191-207. doi: 10.7498/aps.21.191

Catalog

Vol. 59, Issue 6 - 2010-03-20

Metrics

Abstract views: 8232
PDF Downloads: 914
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板