非线性弹性地基上矩形薄板的主参数共振

›› 2005, Vol. 26 ›› Issue (12): 1921-1925.

• Fundamental Theroy and Experimental Research • Previous Articles Next Articles

Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation

YANG Zhi-an^{1, 2}, ZHAO Xue-juan², XI Xiao-yan²

1. School of Mechanical Engineering, Tianjin University, Tianjin 300072, China; 2. Key Laboratory of Structural and Vibration Engineering of Tangshan, Tangshan College, Tangshan 063000, China

Received:2004-06-12 Online:2005-12-10 Published:2014-01-12

Abstract

Abstract: Primary parametric resonance of a parametrically excited simply supported thin rectangular plate on nonlinear elastic foundation is analyzed. The nonlinear vibration equation that has the form of a Mathieu-Duffing’s equation is derived from the Von Karman equation and Galerkin’s method. The method of multiple scales is used to find the averaged equation. Numerical results are presented to illustrate the effect of various parameters including damping parameter, foundation coefficient as well as geometry parameter.

Key words: nonlinear elastic foundation, Galerkin’s method, the method of multiple scales, thin rectangular plate, primary parametric resonance

CLC Number:

TU 470
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YANG Zhi-an , ZHAO Xue-juan , XI Xiao-yan，. Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation[J]., 2005, 26(12): 1921-1925.

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Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation

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