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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.
[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 54 5692］
[34] ］Luo G W, Me J H, Zhu X F, Zhang J G 2008 Chaos Soliton Fract. 36 1340
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[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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 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 物理学报 54 5692］
[34] ］Luo G W, Me J H, Zhu X F, Zhang J G 2008 Chaos Soliton Fract. 36 1340
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