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

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/piezo-magnetic "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 ob-tained using the Radon transform. The expression is further simplified under condi-tions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelec-tric/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.     

磁性斯格明子晶格的磁弹现象与机理

近年来,人们在一些具有手性相互作用的磁性体材料及薄膜中成功观测到具有非平凡拓扑性质的二维自旋结构,称作磁性斯格明子.在大部分情况下,磁性斯格明子自发地聚集成一种晶格结构,称作斯格明子晶格.孤立的斯格明子由于其奇特的拓扑性质以及优异的电流驱动性质等"局域化特征"受到人们的广泛关注.与此相对,斯格明子晶格作为一种新颖的宏观磁性相,可能与材料固有的多场耦合性质发生相互作用进而引发许多奇特的宏观物理现象乃至新性质.在此范畴内,人们发现由于手征磁体内禀的磁弹耦合,斯格明子晶格不但对材料的力学性质产生影响,而且在外力作用下自身具备"层展的弹性性质".本文对相关现象进行梳理,并基于一种针对B20族手征磁体磁弹耦合效应普遍适用的热力学唯象模型,逐一简述对于不同类型的磁弹现象如何建模分析,进而给出其中一部分现象的实验与理论结果比对.最后,对这一领域的发展提出几个可供进一步探索的方向.     

压电压磁复合材料中二维散射问题的解析研究

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）．