压电压磁圆柱壳的自由振动分析

本文基于三维弹性理论，结合状态空间理论和离散奇异卷积算法分析了压电压磁圆柱壳的自由振动问题．圆柱壳的厚度方向被作为状态空间理论的传递方向，同时应用离散奇异卷积算法对面内域进行离散．因此，初始的偏微分运动方程被转化为由一阶常微分方程构成的状态方程．离散奇异卷积算法的引入使得本方法可以处理不同边界条件，从而扩展了常规状态空间方法的应用范围．本文对数值算例的计算验证了此方法的有效性和精确度．

Free Vibration Analysis of Piezoelectric and Piezomagnetic Cylindrical Shells

Based on three-dimensional elasticity theory, semi-analytical solutions for free vibration of piezoelectric and piezomagnetic cylindrical shells have been derived applying a newly developed hybrid analysis, which combines the state space approach (SSA) and the discrete singular convolution (DSC) algorithm. The thickness direction of shells is selected as the transfer direction in SSA, and the DSC is employed to discretize the in-plane domains. Hence, the original partial differential equations are transformed into a state equation consisting of first-order ordinary differential equations. The application of DSC makes it possible to treat various boundary conditions, which cannot be considered in the conventional SSA. Comprehensive numerical examples are presented to validate the present method.