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 引用本文: 王惠明, 丁皓江, 陈云敏. 层合球面各向同性热释电空心球的瞬态响应[J]. 力学学报, 2005, 37(3): 287-294.
Dynamic responses of a multilayer spherically isotropic pyroelectric hollow sphere[J]. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(3): 287-294.
 Citation: Dynamic responses of a multilayer spherically isotropic pyroelectric hollow sphere[J]. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(3): 287-294.

## Dynamic responses of a multilayer spherically isotropic pyroelectric hollow sphere

• 摘要: 运用叠加原理，将层合球面各向同性热释电空心球的球对称动力学问题的解分成准静态和动态两部分，准静态部分首先运用状态空间法给出了显式表达式，然后运用分离变量法、初参数法和特征函数展开技术，给出了动态部分的表示式，再结合内外表面上的电学边界条件和界面上的电学连续条件，导出一个关于时间函数的第二类Volterra积分方程，运用插值法可成功地给出此积分方程的高精度数值解，最终可求得原问题的位移、应力、电位移以及电势的响应. 此方法适用任意层数且各层是任意厚度的层合热释电空心球作用随时间以任意形式变化的球对称温度场. 文中还给出了数值结果.

Abstract: The dynamic solution of a multilayer spherically isotropicpyroelectric hollow sphere for spherically symmetric problem is obtained. Bythe principle of superposition, the solution is divided into two parts: Oneis quasi-static and the other is dynamic. The quasi-static part is obtainedin an explicit form by the state space method, and the dynamic part isderived by the initial parameter method coupled with the separation ofvariables method as well as the orthogonal expansion technique. By using theobtained quasi-static and dynamic parts and utilizing the electric boundaryconditions as well as the electric continuity conditions, a Volterraintegral equation of the second kind with respect to a function of time isderived, which can be solved successfully by means of the interpolationmethod. The displacements, electric potentials and stresses can be finallydetermined. The present method is suitable for a multilayer sphericallyisotropic pyroelectric hollow sphere consisting of arbitrary layers andsubjected to arbitrary spherically symmetric thermal loads. Numericalresults are presented and discussed at the end.

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