Analytical solution to the elastic wave scattering problem caused by a circular inclusion in two dimensional layered inhomogeneous piezoelectric media

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-03-05 DOI:10.1016/j.aml.2025.109546

Enxiang Qu , Hui Qi , Jing Guo

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引用次数: 0

Abstract

The method of complex variable functions is integrated to investigate the steady state problem wherein SH guided waves impinge upon two dimensional layered inhomogeneous piezoelectric media with a circular inclusion, and the corresponding analytical expressions are derived. Specifically, the guided wave expansion technique is employed to formulate the incident wave field of planar SH guided waves. By coupling with the multiple mirror method, the scattering wave field that complies with the requirements of two infinitely long straight boundaries is ascertained. It should be emphasized that these layered straight boundaries must fulfill the stress free and electrically insulating conditions. Subsequently, based on the boundary conditions of stress free, displacement continuity, potential and normal electric displacement continuity that a circular inclusion need to satisfy, infinite linear algebraic equations are further established. Finally, the mathematical analytical expressions for the dynamic stress and electric field intensity around the circular inclusion are obtained.

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二维层状非均匀压电介质中圆形夹杂引起的弹性波散射问题的解析解

采用复变函数法研究了SH导波撞击含圆形夹杂的二维层状非均匀压电介质的稳态问题，并推导了相应的解析表达式。具体地说，利用导波展开技术计算了平面SH导波的入射波场。通过与多镜法的耦合，确定了满足两无限长直线边界要求的散射波场。应该强调的是，这些层状直边界必须满足无应力和电绝缘条件。随后，基于圆包涵体需要满足的无应力、位移连续性、电势和法向电位移连续性的边界条件，进一步建立了无限线性代数方程。最后，得到了圆形夹杂物周围动应力和电场强度的数学解析表达式。

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.