Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation

YANG Zhi-an; ZHAO Xue-juan; XI Xiao-yan

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Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation

更新时间：2026-06-25

- Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation
- Vol. 26, Issue 12, (2005)
- 作者机构：
  
  1. 天津大学机械工程学院,天津,300072
  2. 唐山学院唐山市结构与振动工程重点实验室,唐山,063000
- 作者简介：
- 基金信息：
- DOI：
  CLC： TU470
- Online First：12 January 2014，
  
  Published：2005
- 稿件说明：
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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).
DOI：

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

摘要

分析非线性弹性地基上受参数激励小挠度矩形薄板的主参数共振问题，由冯卡门方程和伽辽金方法得到系统的非线性振动方程，它是杜分-马休型方程，应用非线性振动的多尺度法得到平均方程。数值计算结果表明：阻尼系数、地基系数、几何参数对主参数共振曲线影响明显。

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.

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