| Winkler地基上四边自由矩形薄板的3次超谐波共振与奇异性 |
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| 引用本文： | 杨志安,李文兰,席晓燕.Winkler地基上四边自由矩形薄板的3次超谐波共振与奇异性[J].工程力学,2006,23(10):41-44,29. |
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| 作者姓名： | 杨志安 李文兰 席晓燕 |
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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,唐山,063000;天津大学图书馆,天津,300072 |
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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3次超谐共振情况时的一次近似解以及对应的定常运动,并对其进行数值了计算。对3次超谐共振定常运动分岔响应方程进行了奇异性分析,得到了开折参数平面的转迁集和分岔图。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 奇异性 |
| 文章编号： | 1000-4750（2006）10-0041-04 |
| 收稿时间： | 2005-01-10 |
| 修稿时间： | 2005-01-102005-05-14 |
THREE SUPERHARMONIC RESONANCE AND SINGULARITY OF RECTANGULAR THIN PLATES WITH FOUR SIDES FREE ON WINKLER FOUNDATION |
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| YANG Zhi-an,LI Wen-lan,XI Xiao-yan.THREE SUPERHARMONIC RESONANCE AND SINGULARITY OF RECTANGULAR THIN PLATES WITH FOUR SIDES FREE ON WINKLER FOUNDATION[J].Engineering Mechanics,2006,23(10):41-44,29. |
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| Authors: | YANG Zhi-an LI Wen-lan XI Xiao-yan |
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| Abstract: | According to the Galerkin method, the control equation of rectangular thin plates with four sides free on the Winkler foundation under harmonic excitation is translated into nonlinear vibration equations. Using the method of multiple scales of the nonlinear vibration, the first approximate solutions and corresponding steady state solutions of the three superharmonic resonance of the system are obtained. Numerical calculation is carried out. Singularities of the three superharmonic resonance solution are investigated. The transition variety and bifurcation diagram of unfolding parameter plane are obtained. 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 singularity |
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