四边简支FGM矩形板非线性振动中的内共振

郝育新 张 伟

振动与冲击 ›› 2009, Vol. 28 ›› Issue (6) : 153-154.

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振动与冲击 ›› 2009, Vol. 28 ›› Issue (6) : 153-154.
论文

四边简支FGM矩形板非线性振动中的内共振

  • 郝育新 张 伟
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Nonlinear Vibration of Functionally Graded Material Plate under Different Internal Resonances

  • Hao Yuxin Zhang Wei
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摘要

基于Reddy高阶剪切变形板理论、Galerkin法与Hamilton原理,在同时考虑几何非线性、材料物性参数随温度变化且材料组分沿厚度方向按幂律分布的情况下,通过理论推导建立起四边简支功能梯度材料矩形板受面内与横向简谐载荷共同作用下的非线性运动控制微分方程;在此基础上建立了受热载荷作用下的具有二阶模态的非线性运动控制微分方程。分析了面内静态载荷对于给定参数下系统不同内共振的影响,发现随着面内静态载荷的不同系统会出现1:11:2 1:3的内共振关系。计算结果发现由于不同内共振关系对应的面内静态载荷不同,不同内共振关系下所求得的一阶频率大小各不相同,所对应的瞬态响应也会不同。

Abstract

The nonlinear dynamic response of functionally graded (FGM) rectangular plates under combined transverse and in-plane excitations are investigated under the different internal resonance. The material properties are assumed to be temperature-dependent and vary along the thickness direction. The thermal effect due to one-dimensional temperature gradient is included in the analysis. The governing equations of motion for FGM rectangular plates are derived by using Reddy’s third-order plate theory and Hamilton’s principle. The Galerkin’s approach is utilized to reduce the governing differential equations to a two-degree-of-freedom nonlinear system including quadratic and cubic nonlinear terms, which are then solved numerically by using 4-th order Runge-Kutta algorithm. The resonant case considered herein are 1:1, 1:2 and 1:3 internal resonance and principal parametric resonance-1/2 subharmonic resonance. The effects of plate geometry parameters, in-plane excitations and temperature field on the internal resonance relationship and nonlinear dynamic response of FGM plates are studied. Numerical results show that in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance, the vibration amplitude of the plate center is much greater than the other two cases of the internal resonance.

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mso-bidi-font-size: 12.0pt / mso-font-kerning: 1.0pt / mso-ansi-language: EN-US / mso-fareast-language: ZH-CN / mso-bidi-language: AR-SA / mso-fareast-font-family: 宋体">Functionally graded mater

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郝育新 张 伟. 四边简支FGM矩形板非线性振动中的内共振[J]. 振动与冲击, 2009, 28(6): 153-154
Hao Yuxin Zhang Wei. Nonlinear Vibration of Functionally Graded Material Plate under Different Internal Resonances[J]. Journal of Vibration and Shock, 2009, 28(6): 153-154

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