| Winkler地基上四边自由矩形薄板的主共振与奇异性 |
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| 引用本文： | 杨志安.Winkler地基上四边自由矩形薄板的主共振与奇异性[J].振动与冲击,2006,25(3):105-109,114. |
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| 作者姓名： | 杨志安 |
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| 作者单位： | 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 |
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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，求得了系统满足主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。对主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 |
| 收稿时间： | 2005-01-04 |
| 修稿时间： | 2005-01-042005-03-22 |
PRIMARY RESONANCE AND SINGULARITYOF THE RECTANGULAR THIN PLATE WITH FOUR SIDES FREE ON THE WINKLER FOUNDATION |
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| Yang Zhian.PRIMARY RESONANCE AND SINGULARITYOF THE RECTANGULAR THIN PLATE WITH FOUR SIDES FREE ON THE WINKLER FOUNDATION[J].Journal of Vibration and Shock,2006,25(3):105-109,114. |
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| Authors: | Yang Zhian |
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| Abstract: | According to the Galerkin method,the governing equation of rectangular thin plate with four sides free on the Winkler foundation under lateral harmonic excitation is transformed into nonlinear vibration equation.Using the method of multiple scales of the nonlinenar vibration,the first order approximate solutions and corresponding steady solutions of the primary resonance of the system sre obtained.Numerical calculation is carried out.The influences of the exciting force ,exciting frequency,damping and nonlinear parameters on the system are analyzed.Singularities of the primary resonance solution are investigated.The transition set and bifurcation diagram of the unfolding parameter plane are obtained.Some new dynamical phenomena are revealed. |
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| Keywords: | thin plate with elastic foundation the Galekin method the method of multiple scales nonlinear vibration singularity |
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