{"title":"具有Kelvin-Voigt阻尼和时滞的Rao-Nakra夹层梁模型解的稳定性","authors":"V. Cabanillas, C. Raposo, L. Potenciano-Machado","doi":"10.2298/tam210502006c","DOIUrl":null,"url":null,"abstract":"This paper deals with stability of solution for a one-dimensional model of Rao-Nakra sandwich beam with Kelvin-Voigt damping and time delay given by ?1h1utt ? E1h1uxx ? k(?u + v + awx) ? auxxt ? ?uxxt( ? , t ? ?) = 0, ?3h3vtt ? E3h3vxx + k(?u + v + ?wx) ? bwxxt = 0, ? hwtt + EIwxxxx ? k?(?u + v + ?wx)x ? cwxxt = 0. A sandwich beam is an engineering model that consists of three layers: two stiff outer layers, bottom and top faces, and a more compliant inner layer called ?core layer?. Rao-Nakra system consists of three layers and the assumption is that there is no slip at the interface between contacts. The top and bottom layers are wave equations for the longitudinal displacements under Euler-Bernoulli beam assumptions. The core layer is one equation that describes the transverse displacement under Timoshenko beam assumptions. By using the semigroup theory, the well-posedness is given by applying the Lumer-Phillips Theorem. Exponential stability is proved by employing the Gearhart-Huang-Pr?ss? Theorem.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"24 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Stability of solution for Rao-Nakra sandwich beam model with Kelvin-Voigt damping and time delay\",\"authors\":\"V. Cabanillas, C. Raposo, L. Potenciano-Machado\",\"doi\":\"10.2298/tam210502006c\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with stability of solution for a one-dimensional model of Rao-Nakra sandwich beam with Kelvin-Voigt damping and time delay given by ?1h1utt ? E1h1uxx ? k(?u + v + awx) ? auxxt ? ?uxxt( ? , t ? ?) = 0, ?3h3vtt ? E3h3vxx + k(?u + v + ?wx) ? bwxxt = 0, ? hwtt + EIwxxxx ? k?(?u + v + ?wx)x ? cwxxt = 0. A sandwich beam is an engineering model that consists of three layers: two stiff outer layers, bottom and top faces, and a more compliant inner layer called ?core layer?. Rao-Nakra system consists of three layers and the assumption is that there is no slip at the interface between contacts. The top and bottom layers are wave equations for the longitudinal displacements under Euler-Bernoulli beam assumptions. The core layer is one equation that describes the transverse displacement under Timoshenko beam assumptions. By using the semigroup theory, the well-posedness is given by applying the Lumer-Phillips Theorem. Exponential stability is proved by employing the Gearhart-Huang-Pr?ss? Theorem.\",\"PeriodicalId\":44059,\"journal\":{\"name\":\"Theoretical and Applied Mechanics\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical and Applied Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2298/tam210502006c\",\"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/tam210502006c","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 1
摘要
本文研究具有Kelvin-Voigt阻尼和时滞的Rao-Nakra夹层梁一维模型解的稳定性。E1h1uxx吗?k (?U + v + awx) ?auxxt吗?uxxt (???) = 0, ?3h3vtt ?x + x + kU + v + ?wx ?BWXXT = 0, ?hwtt + EIwxxxx ?k ? (?U + v + ?wx)x ?CWXXT = 0。夹层梁是一种由三层组成的工程模型:两个坚硬的外层,底部和顶部,以及一个更柔顺的内层,称为“核心层”。Rao-Nakra系统由三层组成,假设触点之间的界面没有滑移。顶层和底层是欧拉-伯努利梁假设下纵向位移的波动方程。核心层是在Timoshenko梁假设下描述横向位移的一个方程。利用半群理论,利用Lumer-Phillips定理给出了半群的适定性。利用Gearhart-Huang-Pr?ss?定理。
Stability of solution for Rao-Nakra sandwich beam model with Kelvin-Voigt damping and time delay
This paper deals with stability of solution for a one-dimensional model of Rao-Nakra sandwich beam with Kelvin-Voigt damping and time delay given by ?1h1utt ? E1h1uxx ? k(?u + v + awx) ? auxxt ? ?uxxt( ? , t ? ?) = 0, ?3h3vtt ? E3h3vxx + k(?u + v + ?wx) ? bwxxt = 0, ? hwtt + EIwxxxx ? k?(?u + v + ?wx)x ? cwxxt = 0. A sandwich beam is an engineering model that consists of three layers: two stiff outer layers, bottom and top faces, and a more compliant inner layer called ?core layer?. Rao-Nakra system consists of three layers and the assumption is that there is no slip at the interface between contacts. The top and bottom layers are wave equations for the longitudinal displacements under Euler-Bernoulli beam assumptions. The core layer is one equation that describes the transverse displacement under Timoshenko beam assumptions. By using the semigroup theory, the well-posedness is given by applying the Lumer-Phillips Theorem. Exponential stability is proved by employing the Gearhart-Huang-Pr?ss? Theorem.
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