| 条状功能梯度材料中偏心裂纹对反平面简谐波的散射问题 |
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| 引用本文： | 李琳,周振功,王彪.条状功能梯度材料中偏心裂纹对反平面简谐波的散射问题[J].应用数学和力学,2006,27(6):646-654. |
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| 作者姓名： | 李琳 周振功 王彪 |
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| 作者单位： | 1. 哈尔滨工业大学,复合材料研究所,哈尔滨,150001
2. 中山大学,物理与工程学院,广州,510275 |
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| 基金项目： | 中国科学院资助项目;黑龙江省杰出青年科学基金 |
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| 摘 要： | 利用Sehmidt方法研究了条状功能梯度材料中偏心裂纹对反平面简谐波的散射问题，裂纹垂直于条状功能梯度材料的边界．通过Fourier变换，问题可以转换为对一对未知变量是裂纹表面位移差的对偶积分方程求解．为了求解对偶积分方程，把裂纹表面的位移差展开为Jacobi多项式级数形式，进而得到了功能梯度参数、裂纹位置以及入射波频率对应力强度因子影响的规律．
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| 关 键 词： | 裂纹 弹性波 功能梯度材料 |
| 文章编号： | 1000-0887（2006）06-0646-09 |
| 收稿时间： | 2004-10-15 |
| 修稿时间： | 2006-02-26 |
Scattering of Anti-Plane Shear Waves in a Functionally Graded Material Strip With an Off-Center Vertical Crack |
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| LI Lin,ZHOU Zhen-gong,WANG Biao.Scattering of Anti-Plane Shear Waves in a Functionally Graded Material Strip With an Off-Center Vertical Crack[J].Applied Mathematics and Mechanics,2006,27(6):646-654. |
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| Authors: | LI Lin ZHOU Zhen-gong WANG Biao |
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| Institution: | 1. Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P.R. China; 2. School of Physics and Engineering, Sun Yat-Sen University, Guangzhou 510275, P. R. China |
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| Abstract: | The scattering problem of anti-plane shear waves in a functionally graded material strip with an off-center crack is investigated by use of Schmidt method. The crack is vertically to the edge of the strip. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations that the unknown variable is the jump of the displacement across the crack surfaces. To solve the dual integral equations, the jump of the displacement across the crack surfaces was expanded in a series of Jacobi polynomials. Numerical examples were provided to show the effects of the parameter describing the functionally graded materials, the position of the crack and the frequency of the incident waves upon the stress intensity factors of the crack. |
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| Keywords: | crack elastic wave functionally graded material |
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