| 一类参数激励和外激励联合作用下四边简支薄板的周期解 |
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| 引用本文： | 孙敏,张伟,陈建恩,周艳. 一类参数激励和外激励联合作用下四边简支薄板的周期解[J]. 动力学与控制学报, 2013, 11(2): 149-152 |
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| 作者姓名： | 孙敏 张伟 陈建恩 周艳 |
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| 作者单位： | 北京工业大学机电学院,北京 100124;北京工业大学机电学院,北京 100124;北京工业大学机电学院,北京 100124;北京工业大学机电学院,北京 100124 |
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| 基金项目： | 国家自然科学基金资助项目(11072008),(10732020) |
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| 摘 要： | 研究了一类参数激励和外激励联合作用下四边简支薄板在1:1内共振下的周期解分叉.首先,根据von Karman方程推导出四边简支薄板的运动控制方程,利用Galerkin方法得到参数激励和外激励联合作用下的两个自由度的运动方程.然后,通过引入周期变换和相应的Poincaré映射推广了次谐Melnikov方法.最后,对系统进行数值模拟验证了理论的正确性.
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| 关 键 词： | 周期解 次谐Melnikov函数 周期变换 薄板 |
| 收稿时间： | 2012-06-18 |
| 修稿时间： | 2012-07-02 |
Periodic motions of rectangular thin plate with parametrically and externally excitations |
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| Sun Min,Zhang Wei,Chen Jianen and Zhou Yan. Periodic motions of rectangular thin plate with parametrically and externally excitations[J]. Journal of Dynamics and Control, 2013, 11(2): 149-152 |
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| Authors: | Sun Min Zhang Wei Chen Jianen Zhou Yan |
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| Affiliation: | (College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China ) |
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| Abstract: | The bifurcations of periodic solutions for a parametrically and externally excited rectangular thin plate with 1 ： 1 internal resonance were investigated. First, the equations of motion with two-degree-of- freedom of the rectangular thin plate were derived from the von Karman equation and Galerkin＇s method. Then, based on periodic transformations and Poincare map, the subharmonic Melnikov function was improved to analyze the periodic solutions of four-dimensional non-autonomous systems. Numerical simulations verified the analytical predictions. |
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| Keywords: | periodic solution subharmonic Melnikov function periodic transformation rectangular thin plate |
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