{"title":"Lamb quasi–modes in curved plates","authors":"D. Gridin, R. Craster","doi":"10.1098/rspa.2003.1254","DOIUrl":null,"url":null,"abstract":"Wave propagation in slowly varying elastic waveguides is analysed in terms of mutually uncoupled quasi–modes. These are a generalization of the Lamb modes that exist in a uniform guide to a weakly non–uniform guide. Quasi–modal propagation is dependent upon the wavelength and two geometrical length–scales, that of the longitudinal variations and the guide thickness. By changing these length–scales one enters different asymptotic regimes. In this paper the emphasis is on the mid–frequency regime, where only a few propagating modes can exist. Our aim is to present an asymptotic theory for quasi–modal propagation in a canonical geometry, an arbitrarily curved two–dimensional plate of constant thickness. We derive practically useful asymptotic expressions of the quasi–modes of a weakly curved plate; these are particularly important since an adiabatic approximation for this problem coincides with the expression for the Lamb modes of a flat plate of the same thickness.","PeriodicalId":20722,"journal":{"name":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2004-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"11","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1098/rspa.2003.1254","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 11
Abstract
Wave propagation in slowly varying elastic waveguides is analysed in terms of mutually uncoupled quasi–modes. These are a generalization of the Lamb modes that exist in a uniform guide to a weakly non–uniform guide. Quasi–modal propagation is dependent upon the wavelength and two geometrical length–scales, that of the longitudinal variations and the guide thickness. By changing these length–scales one enters different asymptotic regimes. In this paper the emphasis is on the mid–frequency regime, where only a few propagating modes can exist. Our aim is to present an asymptotic theory for quasi–modal propagation in a canonical geometry, an arbitrarily curved two–dimensional plate of constant thickness. We derive practically useful asymptotic expressions of the quasi–modes of a weakly curved plate; these are particularly important since an adiabatic approximation for this problem coincides with the expression for the Lamb modes of a flat plate of the same thickness.
期刊介绍:
Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.