微分容积法分析复合材料椭圆板的自由振动

Differential cubature method for free vibration analysis of clamped anti-symmetrically laminated elliptical plates

研究用一种高效率高精度的数值方法———微分容积法求解周边固支的反对称角铺设层叠复合材料椭圆板的自由振动,基于经典的薄板理论,首先建立了问题的控制微分方程和相应的边界条件,然后利用微分容积法将控制方程和边界条件转化为一组用域内配点位移表示的线性齐次代数方程,这是经典的线性特征值问题,利用子空间迭代法就可求出振动的固有频率因子,并通过数值算例,展示了方法的收敛性、简单性和有效性,经与已有的数值结果比较发现,本文结果具有很好的精度。

This paper discusses a free vibration study of clamped anti-symmetrically laminated elliptical plates by using a highly efficient and accurate global numerical method:the differential cubature method. The governing differential equations and boundary condition equations are firstly established based on the classical plate theory. Then these equations are transformed into a set of linear homogeneous algebraic equations regarding the displacements of discreted points in the physical domain, by using the differential cubature procedure. This is a typical eigenvalue problem, of which the eigenvalues and eigenvestors can be calculated unmerically. The subspace iterative method is used to search for the dimensionless frequency parameters. The applicability, efficiency, and simplicity of this method are demonstrated through some examples of plate vibration solution. The numerical accuracy is verified by studying the convergence characteristics of plate vibration frequencies and, when possible, by comparing the numerical solutions with existing literature.