General solutions for coupled equations for piezoelectric media

Three general solutions are obtained for the coupled dynamic equations for a transversely isotropic piezoelectric medium. These solutions are expressed in terms of the two functions psi and F, where psi satisfies a second-degree partial differential equation and F a sixth-degree partial differential equation, respectively. If the terms concerning the derivatives of time are removed, the results become three general solutions for the corresponding equilibrium equations, in which the function F can be represented by functions F-i (i = 1, 2, 3), each of which satisfies a second-degree partial differential equation by utilizing a generalized Almansi theorem; and the solution Wang and Zheng [Int. J. Solids Structures 32, 105-115 (1995)] obtained is proved to be consistent with one case of one of the three general solutions. When the constants e(15) = e(31) = e(33) = 0 the piezo-electric coupling is absent; then, two of the solutions reduce to the elasticity general solutions for a transversely isotropic medium, one of which is the result Hu [Acta Scientia Sin. 2(2), 145-151 (1953)] obtained; the other one has not been published. Last, the solution in the limiting explicit form for the problem for a half-space with concentrated loads at the boundary is obtained by utilizing the general solutions. (C) 1996 Elsevier Science Ltd.