弹性地基上四边自由矩形大挠度薄板复杂运动研究

Research on Complex Vibration of Large Deflection of Rectangular Thin Plates with Four Free Edges on Elastic Foundation

考虑具有粘滞阻尼的Winkler地基上四边自由受简谐激励的矩形板的偏微分方程组,找到了满足所有边界条件的近似挠度函数,利用Galerkin方法把偏微分方程表示的非线性动力学方程转化为用常微分方程表示的非线性动力学方程。应用多尺度法求得了系统的主共振解,并对主共振解的静态分岔方程进行了奇异性分析。应用Floquet理论和Melnikov方法分析了系统的全局特性。

Nonlinear dynamical equation of large defletion of thin plates with four free edges on elastic foundation is established.The linear damping and harmonically excitation are considered.By using Galerkin method the nonlinear vibration equation is obtained.By means of the method of multiple scales and singularities theory,the primary resonance solution is obtained and its singularities is investigated.According to Floquet theory and Melnikov function,the general features are studied.