Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (12): 1535-1552 .doi: https://doi.org/10.1007/s10483-008-1202-x

• Articles • 上一篇    下一篇

压电压磁复合材料中二维散射问题的解析研究

胡杨凡1;王彪2   

  1. 1.中山大学 应用力学与工程系,广州 510275;
    2.中山大学 物理与工程学院,广州 510275
  • 收稿日期:2008-09-03 修回日期:2008-09-18 出版日期:2008-12-01 发布日期:2008-12-01
  • 通讯作者: 王彪

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

HU Yang-fan1;WANG Biao2   

  1. 1. Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China; 2. School of Physics and Engineering, Sun Yat-sen University, Guangzhou 510275, P. R. China
  • Received:2008-09-03 Revised:2008-09-18 Online:2008-12-01 Published:2008-12-01
  • Contact: WANG Biao

摘要: 用极化方法分析了含一二维夹杂的无限压电压磁基体中的波动散射问题.以此为目的,首先构建了二维压电压磁“相对体”的极化方法.当一般性波动退减为简谐振动时,极化方法的核心函数退减为二维谐波Green函数.利用氡变换的解析方法,首次求得了二维谐波Green函数的积分表达式,该表达式在低频初始波与小尺度椭圆柱夹杂物的假设下可得到进一步的简化,并最终求得解析解A •D2推导针对同时具有压电以及压磁效应的一般性各向异性材料进行,然后将所得的结果简化到仅针对压电复合材料的情况.以此简化解析解为基础,提供了两个算例,讨论了影响含一二维椭圆柱夹杂的PZT_5H压电陶瓷复合材料的散射截面的各种不同因素(包括夹杂的尺寸、形状效应,材料常数的影响,以及压电效应等.

Abstract: Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.

中图分类号: 

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals