{"title":"含有限尺寸效应的粘弹性介质亚波长自由分层边缘均匀化","authors":"R. Belemou, A. Sbitti, J.-J. Marigo, A. Tsouli","doi":"10.23939/mmc2023.01.010","DOIUrl":null,"url":null,"abstract":"This paper proposes the homogenization for a stratified viscoelastic media with free edge. We consider the effect of two-dimensional periodically stratified slab over a semi-infinite viscoelastic ground on the propagation of shear waves hitting the interface. Within the harmonic regime, the second order homogenization and matched-asymptotic expansions method is employed to derive an equivalent anisotropic slab associated with effective boundary and jump conditions for the displacement and the normal stress across an interface. The reflection coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of layers associated with Neumann boundary conditions.","PeriodicalId":37156,"journal":{"name":"Mathematical Modeling and Computing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Homogenization of subwavelength free stratified edge of viscoelastic media including finite size effect\",\"authors\":\"R. Belemou, A. Sbitti, J.-J. Marigo, A. Tsouli\",\"doi\":\"10.23939/mmc2023.01.010\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes the homogenization for a stratified viscoelastic media with free edge. We consider the effect of two-dimensional periodically stratified slab over a semi-infinite viscoelastic ground on the propagation of shear waves hitting the interface. Within the harmonic regime, the second order homogenization and matched-asymptotic expansions method is employed to derive an equivalent anisotropic slab associated with effective boundary and jump conditions for the displacement and the normal stress across an interface. The reflection coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of layers associated with Neumann boundary conditions.\",\"PeriodicalId\":37156,\"journal\":{\"name\":\"Mathematical Modeling and Computing\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Modeling and Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.23939/mmc2023.01.010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Modeling and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.23939/mmc2023.01.010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
Homogenization of subwavelength free stratified edge of viscoelastic media including finite size effect
This paper proposes the homogenization for a stratified viscoelastic media with free edge. We consider the effect of two-dimensional periodically stratified slab over a semi-infinite viscoelastic ground on the propagation of shear waves hitting the interface. Within the harmonic regime, the second order homogenization and matched-asymptotic expansions method is employed to derive an equivalent anisotropic slab associated with effective boundary and jump conditions for the displacement and the normal stress across an interface. The reflection coefficients and the displacement fields are obtained in closed forms and their validity is inspected by comparison with direct numerics in the case of layers associated with Neumann boundary conditions.