{"title":"Behavior of a wave with absorption at discontinuity: telegrapher’s equation approach","authors":"Marco Nizama, Manuel O. Cáceres","doi":"10.1007/s00707-024-04045-3","DOIUrl":null,"url":null,"abstract":"<div><p>The propagation of a wave packet in a discontinuous medium, one of them with absorption of energy, has been studied analytically. We examined an electromagnetic pulse starting in a free medium and moving toward a dissipative one. In the first medium, the wave is free-moving governed by the wave equation, while in the second medium, the wave is affected by the Joule effect governed by the telegrapher’s equation. We solved the motion at the discontinuity using the Fourier representation for a wave packet in the formalism of a wave attenuated approach. This allowed us to calculate a reflection amplitude in analogy with the ordinary definition at a discontinuity in a medium without dissipation but with different velocities in each medium.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"235 10","pages":"6249 - 6262"},"PeriodicalIF":2.3000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mechanica","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s00707-024-04045-3","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0
Abstract
The propagation of a wave packet in a discontinuous medium, one of them with absorption of energy, has been studied analytically. We examined an electromagnetic pulse starting in a free medium and moving toward a dissipative one. In the first medium, the wave is free-moving governed by the wave equation, while in the second medium, the wave is affected by the Joule effect governed by the telegrapher’s equation. We solved the motion at the discontinuity using the Fourier representation for a wave packet in the formalism of a wave attenuated approach. This allowed us to calculate a reflection amplitude in analogy with the ordinary definition at a discontinuity in a medium without dissipation but with different velocities in each medium.
期刊介绍：
Since 1965, the international journal Acta Mechanica has been among the leading journals in the field of theoretical and applied mechanics. In addition to the classical fields such as elasticity, plasticity, vibrations, rigid body dynamics, hydrodynamics, and gasdynamics, it also gives special attention to recently developed areas such as non-Newtonian fluid dynamics, micro/nano mechanics, smart materials and structures, and issues at the interface of mechanics and materials. The journal further publishes papers in such related fields as rheology, thermodynamics, and electromagnetic interactions with fluids and solids. In addition, articles in applied mathematics dealing with significant mechanics problems are also welcome.
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