| 非线性弹性地基上圆形薄板主参数共振-主共振研究 |
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| 引用本文： | 杨志安.非线性弹性地基上圆形薄板主参数共振-主共振研究[J].工程力学,2008,25(2):78-82. |
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| 作者姓名： | 杨志安 |
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| 作者单位： | 唐山学院唐山市结构与振动工程重点实验室,河北,唐山,063000 |
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| 摘 要： | 研究非线性地基上圆形薄板受简谐激励的非线性振动问题。按照弹性力学理论建立非线性地基上圆形薄板受简谐激励的动力学方程。利用Galerkin方法将其转化为非线性振动方程,它是达芬-马休型方程。应用非线性振动的多尺度法求得系统主参数共振-主共振条件的一次近似解,并进行数值计算。分析阻尼、地基系数、几何参数等对共振响应曲线的影响。比较了两种地基的计算结果。
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| 关 键 词： | 非线性地基 Galerkin方法 多尺度法 主参数共振-主共振 圆板 |
| 文章编号： | 1000-4750（2008）02-0078-05 |
| 收稿时间： | 2006-06-30 |
| 修稿时间： | 2007-06-16 |
STUDY ON PRIMARY PARAMETRIC RESONANCE AND PRIMARY RESONANCE OF A THIN CIRCULAR PLATE ON NONLINEAR FOUNDATION |
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| YANG Zhi-an.STUDY ON PRIMARY PARAMETRIC RESONANCE AND PRIMARY RESONANCE OF A THIN CIRCULAR PLATE ON NONLINEAR FOUNDATION[J].Engineering Mechanics,2008,25(2):78-82. |
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| Authors: | YANG Zhi-an |
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| Abstract: | In order to study primary parametric resonance and primary resonance of a thin circular plate subjected to harmonic excitation on nonlinear foundation by applying elastic theory, nonlinear dynamical equation of the system is established. Nonlinear oscillation equation is obtained based on Galerkin’s method. It is Duffing-Mathieu equation. By means of the method of multiple scales for nonlinear oscillations the approximation solution of primary parametric resonance and primary resonance of the system is acquired. Numerical analysis of the influence of damping, foundation coefficient, and geometric parameter on the system is carried out. The calculation results of two kinds of foundation are compared. |
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| Keywords: | nonlinear foundation Galerkin’s method the method of multiple scales primary parametric resonance and primary resonance circular plate |
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