层状层电介质空间轴对称问题的状态空间解

从横观各向同性压电介质空间轴对称问题的基本方程出发，建立了压电介质空间轴对称问题的状态变量方程，对状态变量方程进行Hankel变换，得到以状态变量表示的单层压电介质在Hankel变换空间中的解，讨论了3种不同特征根的情况，利用提出的解得到了半无限压电体在垂直集中载荷和点电荷作出下的Boussinesq解。利用传递矩阵方法导出了多层压电介质空间轴对称问题解一般解析式。

THE STATE SPACE SOLUTION OF LAYERED SPACE AXISYMMETRIC PIEZOELECTRIC MEDIA

A space axisymmetric electroelastic formulation is developed to study the response of piezoelectric media. The methodology is based on a state space formulation where a particular collection of elastic and electric vaxiables is used to determine the behavior of a layered transversely isotropic piezoelectric media subjected to arbitrary loading conditions. In this paper, the state vector equation of transversely isotropic space axisymmetric piezoelectric media is established in a system of cylindrical coordinates. The state vector equations are a set of partial differential equa- tions. By the use of the Hankel integral transform the state vector equations are transformed into a set of ordinary differential equations. According to the theory of ordinary differential equations and the Cayley-Hamilton theorem, the solutions of state vector equation are obtained which are the product of initial state variables and transfer matrix. The results for three kinds of eigenvalue, i.e.,are presented.Using the solution presented in this paper, Boussineseq's solution of semi-infinite piezoelectric layer is presented. For two or more layers space axisymmetric piezoelectric media using the interface continuity conditions the intermediate state vector is eliminated. The general formulation of the solution for more layers space axisymmetric piezoelectric media is given using the method of transfer matrix.