求解任意形状厚板自由振动的微分容积法

用一种新型的数值方法－微分容积法求解具有任意形状的厚板自由振动问题。该方法的基本思想是将任意一个线性微分算子对函数的作用值如一个连续函数或其任意阶偏导数、或其线性组合在某点处的值表示为域内各点函数值的线性加权组合，如此可将问题的控制方程和边界条件离散成为一组线性齐次代数方程。这是一典型的特征值问题，其特征值可用子空间迭代法求解。文中给出了详细的计算公式，用一些数值算例说明了该方法求解中厚板自由振动问题的可行性、有效性和通用性，并通过与有关文献比较验证了该方法的数值精度。

Differential Cubature Method for Free Vibration Analysis of Arbitrary Shaped Thick Plates

In this paper, a new numerical solution technique, the d ifferential cubature method is applied to solve the free vibration problems of a rbitrary shaped thick plates. The basic idea of the solution technique is to exp ress a linear differential operation such as a continuous function or any orders of partial derivatives of multi-variable function as a weighted linear sum of discrete function values chosen within the overall domain of a problem. By using the differential cubature procedure, the governing differential equations and b oundary conditions are transformed into sets of linear homogeneous algebraic equ ations. This is an eigenvalue problem, of which the eigenvalues can be calculate d numerically. The subspace iterative method is employed in search of the free v ibration frequency parameters. Detailed formulations are presented, and the meth od is examined here for its suitability for solving the vibration problems of mo derately thick plates governing by the Mindlin shear deformation theory. The app licability, efficiency and simplicity of the method are demonstrated through sol ving some example plate vibration problems of different shapes. The numerical ac curacy of the method is ascertained by comparing the vibration frequency solutio ns with existing literatures.