Interaction of anti‐plane shear waves with two collinear cracks in 1D hexagonal piezoelectric quasicrystals

IF 2.3 4区工程技术 Q1 MATHEMATICS, APPLIED

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik Pub Date : 2023-10-13 DOI:10.1002/zamm.202300393

Sourav Kumar Panja, Subhas Chandra Mandal

引用次数: 0

Abstract

Abstract The present article presents the interaction of anti‐plane shear waves by two collinear cracks in one dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs). With the aid of Fourier transform, the mixed boundary value problem (MBVP) is transformed into three pairs of dual integral equations, which are solved analytically by Hilbert transform. The explicit expressions for dynamic stress intensity factors (DSIFs) of phonon and phason fields, crack opening displacement (COD) and electric displacement (ED) are derived in closed form and some special cases are studied. Numerical values of DSIFs of phonon and phason fields, COD and ED are plotted to show the effect of crack length and electric boundary condition. Moreover, the DSIFs of phonon field and COD are represented graphically for single crack.

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一维六方压电准晶体中反平面剪切波与两个共线裂纹的相互作用

摘要本文研究了一维六边形压电准晶体(pqc)中两个共线裂纹与反平面剪切波的相互作用。利用傅里叶变换，将混合边值问题转化为三对对偶积分方程，用希尔伯特变换解析求解。推导了声子场和相场的动应力强度因子(DSIFs)、裂纹张开位移(COD)和电位移(ED)的封闭表达式，并对一些特殊情况进行了研究。绘制了声子场、相场、COD和ED的dsfs数值，以反映裂纹长度和电边界条件的影响。此外，还用图形表示了单裂纹声子场和COD的DSIFs。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik 数学-力学

CiteScore

3.30

自引率

8.70%

发文量

199

审稿时长

3.0 months

期刊介绍： ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.