任意四边形厚板的自由振动

本文用样条最小二乘法求解任意四边形厚板的自由振动问题，首先通过坐标变换将任意四边形区域映射为一单位正方形区域，然后用满足边界条件的五次样条函数作为试函数代人控制方程得到残值，用最小二乘法消去残值，导出求解固有频率的特征方程，并用子空间迭代法求得圆频率，数值算例表明，该方法收敛较快，精度较高。

Free Vibration of Arbitrary Quadrilateral Thick Plates

In this paper, a free vibration study of arbitrary quadrilateral thick plates by the spline least spuare method was presented. The Reissner-Mindlin shear deformation theory was employed. Firstly, the arbitrary quadrilateral physical domain was mapped onto a basic square computational domain by using the parametric mapping concept, and then the B-5 spline functions were used as trial functions which can satisfy all boundary conditions. By eliminating the residuals obtained from the governing equations, the characteristic equation can be derived. The subspace iterative method was employed to search the vibration frequencies. Several numerical examples demonstrate the convergency and accuracy of this method.