The study of modified method of multiple scales for primary resonance of annular plate electromechanical coupling strong nonlinear system
Yang Zhi’an1, Li Xi 2, Meng Jiajia2
1. Key Laboratory of Structure and Vibration of Tangshan College, Tangshan College, Tangshan 063000, China;
2. School of Mechanical Engineering,Tianjin University,Tianjin 300072,China;
3. College of Mechanical Engineering, Hebei United University, Tangshan 063009, China
Abstract：In order to study primary resonance of annular plate electromechanical coupling strong nonlinear system by applying elastic theory, the nonlinear dynamical equation of the system is established. Nonlinear oscillation equation is obtained based on the Galerkin’s method. It is Duffing-Mathieu equation with two external excitation frequencies. By means of modified method of multiple scales the approximation solutions of primary resonance of the system are acquired. Numerical analysis of the influence of different parameter is carried out.
收稿日期: 2014-07-09
出版日期: 2015-10-15
引用本文:
杨志安1,李熙 2，孟佳佳3. 改进多尺度法求解环形极板机电耦合强非线性系统主共振的研究[J]. 振动与冲击, 2015, 34(19): 208-212.
Yang Zhi’an1, Li Xi 2, Meng Jiajia2. The study of modified method of multiple scales for primary resonance of annular plate electromechanical coupling strong nonlinear system. JOURNAL OF VIBRATION AND SHOCK, 2015, 34(19): 208-212.
[1] 邱家俊. 机电偶联动力系统非线性振动[M]. 北京: 科学出版社, 1996.
QIU Jiajun. Nonlinear oscillation of coupled mechanical and electric dynamics system [M]. Beijing: Science press, 1996.
[2] A. Love. A treatise on the mathematical theory of elasticity [J]. Dover Publications, New York, 1944.
[3] T.Irie, G.Yamada, Y.Muramoto. Natural frequencies of in-plane vibration of annular plates [J]. Journal of Sound and Vibration, 1984, 97(1):171-175.
[4] G. Ambati, J.F.W.Bell, J.C.K.Sharp. In-plane vibration of annular rings [J]. Journal of Sound and Vibration, 1976, 47:425-432.
[5] Haider N. Arafat, Ali H. Neyfeh. Combination internal resonances in heated annular plates [J]. Nonlinear Dynamics, V.37, N.4 285-306, 2004.
[6] Haider N. Arafat, Ali H. Neyfeh. Modal interations in the vibration of a heated annular plate [J]. International Journal of Nonlinear Mechanics, V.39 N.10, 1671-1685, 2004.
[7] 熊蕊, 刘向东. 含PID控制器的迟滞非线性控制系统的主共振及奇异性[J]. 振动与冲击, 2014, 33(8):72-77.
XIONG Rui, LIU Xiangdong. Principal resonance and singularity of a hysteretic nonlinear control system with a PID controller [J]. Journal of Vibration and Shock, 2014, 33(8):72-77.
[8] 杨志安, 贾尚帅. RLC串联电路与微梁耦合系统的吸合压电与电震荡[J]. 应用力学学报, 2010, 27(4):721-726.
YANG Zhian, JIA Shangshuai. Pull-in voltage and electric oscillations of RLC series circuit and microbeam coupled system [J]. Chinese Journal of Applied Mechanics, 2010, 27(4):721-726.
[9] 杨志安, 贾尚帅. RLC串联电路与微梁耦合系统1︰2内共振分析[J]. 应用力学学报, 2010, 27(1):80-85.
YANG Zhian, JIA Shangshuai. Analysis of the 1:2 internal resonance of coupled RLC circuit and microbeam system [J]. Chinese Journal of Applied Mechanics, 2010, 27(1):80-85.
