General solutions for coupled equations for piezoelectric media
General solutions for coupled equations for piezoelectric media
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DOI：
10.1016/0020-7683(95)00152-2
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发表时间：
1996-07
影响因子：
3.6
通讯作者：
Haojiang Ding;Chenbuo;Liangjian
中科院分区：
文献类型：
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作者：
Haojiang Ding;Chenbuo;Liangjian
得到了横观各向同性压电介质耦合动力学方程的三种通解。这些解用两个函数F和F表示，其中F和F分别满足二阶偏微分方程和六阶偏微分方程。如果去掉关于时间导数的项，结果就变成相应平衡方程的三个通解，其中函数F可用函数Fi表示（i = 1，2，3），其中的每一个通过利用广义Almansi定理满足二次偏微分方程;并证明了Wang和Zheng [Int.J.SolidsStructures32，105-115（1995）]所得到的解与三个通解之一的一种情况是一致的。当常数e_（15）= e_（31）= e_（33）= 0时，压电耦合不存在，则有两个解归结为横观各向同性介质的弹性通解，其中一个是Hu [Acta Scientia Sin.2（2），145-151（1953）]的结果，另一个尚未发表。最后，利用一般解得到了边界上有集中荷载的半空间问题的极限显式解。
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 ψ and F, where ψ 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 Fi(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 Structures32, 105–115 (1995)] obtained is proved to be consistent with one case of one of the three general solutions. When the constants e15= e31= e33= 0 the piezo-electric coupling is absent; then, two of the solutions reduce to the elasticity general solutions for a transversely isotropie 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.