Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

doi:10.1088/1674-1056/20/6/060501

Abstract The resonant response of a single-degree-of-freedom nonlinear vibro-impact oscillator with a one-sided barrier to a narrow-band random parametric excitation is investigated. The narrow-band random excitation used here is a bounded random noise. The analysis is based on a special Zhuravlev transformation, which reduces the system to one without impacts, thereby permitting the applications of random averaging over "fast" variables. The averaged equations are solved exactly and an algebraic equation of the amplitude of the response is obtained for the case without random disorder. The methods of linearization and moment are used to obtain the formula of the mean-square amplitude approximately for the case with random disorder. The effects of damping, detuning, restitution factor, nonlinear intensity, frequency and magnitude of random excitations are analysed. The theoretical analyses are verified by numerical results. Theoretical analyses and numerical simulations show that the peak response amplitudes will reduce at large damping or large nonlinear intensity and will increase with large amplitude or frequency of the random excitations. The phenomenon of stochastic jump is observed, that is, the steady-state response of the system will jump from a trivial solution to a large non-trivial one when the amplitude of the random excitation exceeds some threshold value, or will jump from a large non-trivial solution to a trivial one when the intensity of the random disorder of the random excitation exceeds some threshold value.

Keywords: nonlinear vibro-impact system resonance response random averaging method stochastic jump

Received: 12 January 2010
Revised: 11 June 2010
Accepted manuscript online:

PACS:

05.45.-a

(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10772046 and 50978058) and Natural Science Foundation of Guangdong Province of China (Grant No. 102528000010000).

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Su Min-Bang (苏敏邦), Rong Hai-Wu (戎海武) Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation 2011 Chin. Phys. B 20 060501

[1]	Shaw S W and Holmes P J 1983 emphJ. Appl. Mech. 50 849
[2]	Luo G W and Xie J H 2003 emph Phys. Lett. A 313 267
[3]	Luo G W 2004 emphPhys. Lett. A 323 210
[4]	Luo G W, Zhang Y L and Yua J N 2006 emphJ. Sound Vib. 292 242
[5]	Luo G W and Xie J H 2002 emphInt. J. Nonlinear Mech. 37 19
[6]	Xie J and Ding W 2005 emphInt. J. Nonlinear Mech. 40 531
[7]	Bernardon M D 2001 emphPhys. Rev. Lett. 86 2553
[8]	Li M, Ma X K, Dai D and Zhang H 2005 emphActa Phys. Sin. 54 1084 (in Chinese)
[9]	Nordmark A B 1991 emphJ. Sound Vib. 145 279
[10]	Feng J Q, Xu W and Niu Y J 2010 emphActa Phys. Sin. 59 157 (in Chinese)
[11]	Weger J de, Water W van de and Molenaar J 2000 emphPhys. Rev. E 62 2030
[12]	Wang L, Xu Wei and Li Y 2008 emphChin. Phys. B 17 2446
[13]	Dankowicz H and Zhao X 2005 emphPhysica D 202 238
[14]	Metrikyn V S 1970 emphRadiofizika 13 4 (in Russian)
[15]	Stratonovich R L 1963 emphTopics in the Theory of Random Noise (New York: Gordon and Breach) p. 1
[16]	Dimentberg M F 1988 emphStatistical Dynamics of Nonlinear and Time-Varying Systems (Taunton: Research Studies Press, UK)
[17]	Jing H S and Sheu K C 1990 emphJ. Sound Vib. 141 363
[18]	Rong H W, Wang X D, Xu W and Fang T 2008 emphActa Phys. Sin. 57 6888 (in Chinese)
[19]	Huang Z L, Liu Z H and Zhu W Q 2004 emphJ. Sound Vib. 275 223
[20]	Feng J Q, Xu W, Rong H W and Wang R 2009 emphInt. J. Nonlinear Mech. 44 51
[21]	Zhuravlev V F 1976 emphMechanics of Solids 11 23
[22]	Iourtchenko D V and Dimentberg M F 2001 emphJ. Sound Vib. 248 913
[23]	Feng Q and He H 2003 emphEuro. J. Mech. A: Solids 22 267
[24]	Iourtchenko D V and Song L L 2006 emphInt. J. Nonlinear Mech. 41 447
[25]	Dimentberg M F and Iourtchenko D V 2004 emphNonlinear Dyn. 36 229
[26]	Dimentberg M F, Iourtchenko D V and Vanewijk O 1998 emphNonlinear Dyn. 17 173
[27]	Rong H W, Wang X D, Xu W and Fang T 2009 emphJ. Sound Vib. 327 173
[28]	Rong H W, Wang X D, Xu W and Fang T 2009 emphPhys. Rev. E 80 026604
[29]	Stratonovich R L 1967 emphTopics in the Theory of Random Noise (New York: Gordon and Breach) p. 2
[30]	Lin Y K and Cai G Q 1995 emphProbabilistic Structural Dynamics: Advanced Theory and Applications (New York: Mc-Graw-Hill)
[31]	Dimentberg M F, Hou Z, Noori M and Zhang W 1996 emphJ. Sound Vib. 192 621
[32]	Zhu W Q 1992 emphRandom Vibration (Beijing: Science Press) (in Chinese)
[33]	Shinozuka M 1972 emphJ. Sound Vib. 25 111

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Resonance response of a single-degree-of-freedom nonlinear vibro-impact system to a narrow-band random parametric excitation

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