粘弹性地基上考虑耦合效应四边自由矩形薄板的非线性自由振动分析

Research on nonlinear free vibration for the rectangular thin plate with four edges free including the coupled effect of viscoelastic foundation

基于Hamilton能量变分原理和薄板的基本假设,考虑地基阻尼的影响,建立了双参数粘弹性地基上考虑耦合效应的四边自由矩形薄板的非线性自由振动方程以及板域外的控制方程.应用瑞利-里兹法及循环迭代对方程进行求解,探讨了地基阻尼、地基弹性模量以及板的结构参数对双参数粘弹性地基上四边自由矩形薄板的非线性自由振动特性的影响,得出了双参数粘弹性地基两典型参数随时间的变化关系.

Based on the Hamilton energy variational principle and the theory of sheet,considering coupling of double parameters viscoelastic foundation and four edges free of rectangular thin plates,the nonlinear free vibration control equations inside and outside plates are set up.The differential equations have been solved by methods of Riley-Leeds and iteration.Effects of foundation damping and elastic modulus,and the structure parameters of plates on the nonlinear free vibration characteristics of thin plates are analyzed.The relations betweeen two typical parameters of the double parameters（viscoelastic foundation and the time）are obtained.