层合压电压磁耦合弹性介质圆板的状态变量解

A state vector solution to thick laminated circular plate of piezoelectric,piezomagneto and elastic media

从横观各向同性层状压电、压磁耦合弹性介质材料的基本方程出发 ,导出了压电、压磁圆板在轴对称变形中的状态变量方程 ,并对其进行有限 Hankel变换 ,得到一组常系数的常微分方程 ,再通过 Caylay-Hamilton原理和利用传递矩阵方法导出了层合压电、压磁耦合弹性介质圆板的状态变量解 .

The methodology is based on a state space formulation where a particular collection of elastic,electric and magnetic variables are used to determine the behavior of a layered transversely isotropic subjected to piezoelectric,piezomagnetic and elastic media under arbitrary loading conditions.The state vector equation of transversely isotropic space for thick laminated circular plate of piezoelectric,piezomagnetic and elastic media is established.By the use of the Hankel integral transform in finity the state vector equations are transformed into a set of ordinary differential equations.According to the theory of ordinary differential equation and the Caylay-Hamilton theorem,the solutions of state vector equation are obtained which are the product of initial state variables and transfer matrix.The general formulation of the solution for thick laminated circular plate of piezoelectric,peizomagnetic and elastic media is given using the method of transfer matrix.