{"title":"A modified multi-directional iterative mirroring method for SH waves propagation in rectangular sealed plate with a circular surface crack","authors":"Zhiyu Fan, Hui Qi, Jing Guo","doi":"10.1016/j.aml.2024.109321","DOIUrl":null,"url":null,"abstract":"<div><div>This study proposes an exact analytical approach for investigating the steady-state and transient wave dynamic propagation characteristics in frequency and time domain of rectangular sealed plate with a circular surface crack under anti-plane point source wave dynamic load. By introducing revised factor, a modified multi-directional iterative mirroring method is proposed to address the partial differential governing equations of wave propagation with boundary value conditions. Based on wave function expansion method, the scattering wave function is derived after decoupling the governing equation. Fourier integral expansion method is used to solve the infinite linear algebraic boundary equation composed of boundary value conditions. The accuracy of analytical method is verified by numerical calculation and finite element simulation. The results show that the sealed coupled waves have significant effects on dynamic stress concentration and abrupt displacement change.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"160 ","pages":"Article 109321"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965924003410","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
This study proposes an exact analytical approach for investigating the steady-state and transient wave dynamic propagation characteristics in frequency and time domain of rectangular sealed plate with a circular surface crack under anti-plane point source wave dynamic load. By introducing revised factor, a modified multi-directional iterative mirroring method is proposed to address the partial differential governing equations of wave propagation with boundary value conditions. Based on wave function expansion method, the scattering wave function is derived after decoupling the governing equation. Fourier integral expansion method is used to solve the infinite linear algebraic boundary equation composed of boundary value conditions. The accuracy of analytical method is verified by numerical calculation and finite element simulation. The results show that the sealed coupled waves have significant effects on dynamic stress concentration and abrupt displacement change.
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.
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