{"title":"纵波在弹性杆上引起的突发性地基破坏","authors":"I. Shatskyi, V. Perepichka, M. Vaskovskyi","doi":"10.2298/TAM200615001S","DOIUrl":null,"url":null,"abstract":"We study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein?Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"61 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Longitudinal waves in an elastic rod caused by sudden damage to the foundation\",\"authors\":\"I. Shatskyi, V. Perepichka, M. Vaskovskyi\",\"doi\":\"10.2298/TAM200615001S\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein?Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.\",\"PeriodicalId\":44059,\"journal\":{\"name\":\"Theoretical and Applied Mechanics\",\"volume\":\"61 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Applied Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/TAM200615001S\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/TAM200615001S","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
Longitudinal waves in an elastic rod caused by sudden damage to the foundation
We study the problem of propagating longitudinal waves in an elastic rod connected to a locally damaged foundation through a thin elastic layer. The motion of the rigid foundation blocks is considered predetermined. We formulated the initial-boundary problem for the Klein?Gordon equation with a discontinuous right-hand side. The nonstationary fields of displacements, velocities, and deformations were investigated by the Laplace integral transformation method. Examples of sudden divergence of fragments of the foundation by a given value and their mutual separation at a constant speed are considered.
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