Dual equations and solutions of I-type crack of dynamic problems in piezoelectric materials  

作　　者：边文凤 王彪 

机构地区：[1]Postdoctoral Flow Station of Materials Science and Engineering,Harbin Institute of Technology,Harbin 150001,P. R. China [2]School of Physics and Engineering,Sun Yat-Sen University,Guangzhou 510275,P. R. China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第6期731-739,共9页应用数学和力学（英文版）

摘　　要：This paper firstly works out basic differential equations of piezoelectric materials expressed in terms of potential functions, which are introduced in the very beginning. These equations are primarily solved through Laplace transformation, semiinfinite Fourier sine transformation and cosine transformation. Secondly, dual equations of dynamic cracks problem in 2D piezoelectric materials are established with the help of Fourier reverse transformation and the introduction of boundary conditions. Finally, according to the character of the Bessel function and by making full use of the Abel integral equation and its reverse transform, the dual equations are changed into the second type of Fredholm integral equations. The investigation indicates that the study approach taken is feasible and has potential to be an effective method to do research on issues of this kind.This paper firstly works out basic differential equations of piezoelectric materials expressed in terms of potential functions, which are introduced in the very beginning. These equations are primarily solved through Laplace transformation, semiinfinite Fourier sine transformation and cosine transformation. Secondly, dual equations of dynamic cracks problem in 2D piezoelectric materials are established with the help of Fourier reverse transformation and the introduction of boundary conditions. Finally, according to the character of the Bessel function and by making full use of the Abel integral equation and its reverse transform, the dual equations are changed into the second type of Fredholm integral equations. The investigation indicates that the study approach taken is feasible and has potential to be an effective method to do research on issues of this kind.

关 键 词：piezoelectric material dynamic crack potential function coupled integral equation integral transformation 

分 类 号：O346.1[理学—固体力学]