计入剪切变形板的自由振动求解方法

Solution of the free vibration of plates allowing for shear deformation

利用边界元法和有限元法混合分析计入剪切变形板的自由振动,引入Reissner型板自由振动基本方程,得出弯曲静力基本解,进而离散域内惯性力积分项,导出板自由振动的代数特征值方程,从而可求出固有频率及相应的振型。以四边简支方板对比分析、实验,证实计算精度可提高一阶,同时该方法具有无须对插值函数求一阶导数的优点。

The paper deals with the free vibration of the plate allowing for shear deformation by combining the boundary element method and the finite element method. The basic equation of the natural vibration of the Reissner's plate is used for getting the fundamental solution of the bending static. The algebraic equation of characteristic values of the plate free vibration is obtained by discretizing the integral term of the inertial force in the field. Then the natural frequency and correspondent vibration mode are gained. The method of linear interpolation is used for the boundary element. The simply supported square plate is taken as an example to make a comparison between the presented method and the other related methods. The result shows that the calculation accuracy is raised by one order with the presented method,and it is unnecessary to solve the first-order derivative of the interpolating function.