Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials

BIAN Wen-feng; WANG Biao

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BIAN Wen-feng, WANG Biao. Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(6): 651-658.

Citation:

BIAN Wen-feng, WANG Biao. Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(6): 651-658.

Citation:

BIAN Wen-feng, WANG Biao. Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials[J]. Applied Mathematics and Mechanics, 2007, 28(6): 651-658.

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Dual Equations and Solutions of Ⅰ-Type Crack of Dynamic Problems in Piezoelectric Materials

BIAN Wen-feng¹,
WANG Biao²

Postdoctoral Flow Station of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, P. R. China;

Received Date: 2005-10-18
Rev Recd Date: 2007-03-30
Publish Date: 2007-06-15

Abstract

Abstract

Firstly,basic differential equations of piezoelectric materials expressed in terms of the potential functions,which are introduced in the very beginning,were worked out.Then these equations were primarily solved through Laplace transformation,seiminfinite Fourier sine transformation and cosine transformation.After that,the dual equations of dynamic cracks problem in the 2D piezoelectric materials were founded 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 ful use of Abel integral equation and its reverse transform,the dual equations were 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.
- piezoelectric material,
- dynamic crack,
- potential function,
- coupled integral equations,
- integral transformation

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References(12)

References

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