超椭圆中厚板的自由振动

本文用一种新型的数值方法棗微分容积法求解任意边界条件下超椭圆形中厚板的自由振动问题。通过微分容积法将中厚板自由振动的控制微分方程和边界条件离散成为一组齐次的线性代数方程,这是一典型的特征值问题,用子空间迭代法可求出其特征值和特征向量。文中通过一些数值算例研究了该方法的收敛性和数值精度,展示了该方法的可行性和有效性。

ON FREE VIBRATION OF THICK SUPERELLIPTICAL PLATES

This paper presents a free vibration study of moderately thick super-elliptical plates with various boundary constraints using the differential cubature method. The differential cubature method is a numerical procedure which expressing a linear operation of a continuous function or any orders of partial derivatives of multivariable function or combinations of them as a weighted linear sum of discrete function values within the overall domain of a problem. Through this new numerical procedure, the equilibrium governing equations and boundary conditions are transformed into a set of homogeneous linear algebraic equations about displacements at all discrete points. This is a typical eigenvalue problem, of which the eigenvalues can be calculated by the subspace iteration method. The applicability and the efficiency of this method are demonstrated through the convergence and comparison studies for the first five frequency parameters of super-elliptical plates with different boundary conditions.