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非线性弹性地基上矩形薄板的主参数共振
引用本文:杨志安,赵雪娟,席晓燕.非线性弹性地基上矩形薄板的主参数共振[J].岩土力学,2005,26(12):1921-1925.
作者姓名:杨志安  赵雪娟  席晓燕
作者单位:1. 天津大学,机械工程学院,天津,300072;唐山学院唐山市结构与振动工程重点实验室,唐山,063000
2. 唐山学院唐山市结构与振动工程重点实验室,唐山,063000
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。

关 键 词:非线性弹性地基  Galerkin方法  多尺度法  矩形薄板  主参数共振
文章编号:1000-7598-(2005)12-1921-05
收稿时间:2004-06-12
修稿时间:2004-11-20

Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation
YANG Zhi-an,ZHAO Xue-juan,XI Xiao-yan.Primary parametric resonance of thin rectangular plate on nonlinear elastic foundation[J].Rock and Soil Mechanics,2005,26(12):1921-1925.
Authors:YANG Zhi-an  ZHAO Xue-juan  XI Xiao-yan
Institution: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
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.
Keywords:nonlinear elastic foundation  Galerkin’s method  the method of multiple scales  thin rectangular plate  primary parametric resonance  
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