压电压磁复合材料中二维散射问题的解析研究  

Solution of the Two Dimensional Scattering Problem in Piezoelectric/Piezomagnetic Media by Polarization Method

作　　者：胡杨凡[1] 王彪[2] 

机构地区：[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

出　　处：《应用数学和力学》2008年第12期1395-1410,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(1073210010572155);广东科学与技术局资助项目(2006A11001002);中国教育部博士生基金资助项目(2006300004111179)

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.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).Using the 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 two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ was formulated for the first time. For simple harmonic motion, the kernel of the polarization method reduces to the 2-D time-harmonic Green＇s function, which is deduced using the Radon transform. The formalism was further simplified under certain conditions （low frequency of the incident wave and small diameter of the inclusion）, where some explicit analytical expressions were obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites were given first, followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results were provided for an elliptical cylindrical inclusion in a PZT-5H-matrices, iUustrating the effect of different factors （including size effect, shape effect, effect of the material properties, and piezoelectric effect ） on the scattering cross-section.

关 键 词：散射 压电压磁复合材料 极化方法 动力学Green函数 二维问题 氡变换 各向异性材料 

分 类 号：O347.4[理学—固体力学] O302[理学—力学]