| Winkler地基上四边自由矩形薄板的1/3次亚谐波共振 |
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| 引用本文： | 范佳,杨志安,孟宪举.Winkler地基上四边自由矩形薄板的1/3次亚谐波共振[J].河北理工学院学报,2005,27(3):134-140. |
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| 作者姓名： | 范佳 杨志安 孟宪举 |
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| 作者单位： | [1]河北理工大学机械工程学院,河北唐山063009 [2]唐山学院结构与振动实验室,河北唐山063000 |
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| 摘 要： | 通过Galerkin方法,将Winkler地基上四边自由受横向简谐激励矩形薄板的控制微分方程转化为非线性振动方程.应用非线性振动的多尺度法,求得了系统满足1/3次严谐波共振情况时的一次近似解以及对应的定常运动,并对其进行数值计算,分析了激振力、调谐值、阻尼系数、非线性参数对系统的影响,揭示了一些新的动力学现象.
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| 关 键 词： | 弹性地基薄板 Galerkin方法 多尺度法 非线性振动 |
| 文章编号： | 1007-2829（2005）03-0134-07 |
| 收稿时间： | 2004-10-25 |
| 修稿时间： | 2004年10月25 |
Subharmonic of the rectangular Thin plane of four sides free on the winkler foundation |
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| FAN Jia ,YANG Zhi-an, MENG Xian-ju.Subharmonic of the rectangular Thin plane of four sides free on the winkler foundation[J].Journal of Hebei Institute of Technology,2005,27(3):134-140. |
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| Authors: | FAN Jia YANG Zhi-an MENG Xian-ju |
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| Institution: | 1. College of Mechanical Engineering, Hebei Polytechnic, Tangshan Hebei 063009, China ; 2. Tangshan College, Tangshan Hebei 063009, China |
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| Abstract: | According to the Galerkin method, the control equation of rectangular thin plane of four sides free on the Winkler foundation with harmonic excitation is translated into nonlinear vibration equation. Using the method of multiple scales of the nonlinear vibration, the first approximate solutions and corresponding state solutions of the subharmonic of the system are obtained. Numerical calculation is carried out. The influences of the excitation, dunting, damping and nonlinear parameters are analyzed. Some new dynamics phenomena are pointed out. |
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| Keywords: | elastic foundation thin plane the Galerkin method the method of multiple scales nonlinear vibration |
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