{"title":"半各向同性热弹性介质中的耦合谐波平面波","authors":"E. V. Murashkin, Yu. N. Radayev","doi":"10.1134/S0025654424700316","DOIUrl":null,"url":null,"abstract":"<p>The present paper deals with problems of propagation of plane harmonic coupled waves of temperature increment, translational and spinor displacements in a semi-isotropic thermoelastic solid. The requisite constitutive and differential equations of semi-isotropic solids are revisited. Dispersion equation for the wavenumbers of plane harmonic coupled thermoelastic longitudinal waves (bicubic algebraic equation) are obtained and analyzed. Dispersion equations for the transverse waves (equation of the 8th algebraic degree) are splitted into two algebraic quartic equations and then solved. For a longitudinal wave, the complex amplitudes of temperature increment, translational displacements and spin–vector are coupled, unlike a transverse wave. The roots of mentioned algebraic equations are calculated by using the Wolfram Mathematica 13 symbolic computing system. The normal wavenumbers with positive real part are discriminated.</p>","PeriodicalId":697,"journal":{"name":"Mechanics of Solids","volume":"59 4","pages":"2387 - 2394"},"PeriodicalIF":0.6000,"publicationDate":"2024-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Coupled Harmonic Plane Waves in a Semi-Isotropic Thermoelastic Medium\",\"authors\":\"E. V. Murashkin, Yu. N. Radayev\",\"doi\":\"10.1134/S0025654424700316\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The present paper deals with problems of propagation of plane harmonic coupled waves of temperature increment, translational and spinor displacements in a semi-isotropic thermoelastic solid. The requisite constitutive and differential equations of semi-isotropic solids are revisited. Dispersion equation for the wavenumbers of plane harmonic coupled thermoelastic longitudinal waves (bicubic algebraic equation) are obtained and analyzed. Dispersion equations for the transverse waves (equation of the 8th algebraic degree) are splitted into two algebraic quartic equations and then solved. For a longitudinal wave, the complex amplitudes of temperature increment, translational displacements and spin–vector are coupled, unlike a transverse wave. The roots of mentioned algebraic equations are calculated by using the Wolfram Mathematica 13 symbolic computing system. The normal wavenumbers with positive real part are discriminated.</p>\",\"PeriodicalId\":697,\"journal\":{\"name\":\"Mechanics of Solids\",\"volume\":\"59 4\",\"pages\":\"2387 - 2394\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mechanics of Solids\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S0025654424700316\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mechanics of Solids","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1134/S0025654424700316","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
Coupled Harmonic Plane Waves in a Semi-Isotropic Thermoelastic Medium
The present paper deals with problems of propagation of plane harmonic coupled waves of temperature increment, translational and spinor displacements in a semi-isotropic thermoelastic solid. The requisite constitutive and differential equations of semi-isotropic solids are revisited. Dispersion equation for the wavenumbers of plane harmonic coupled thermoelastic longitudinal waves (bicubic algebraic equation) are obtained and analyzed. Dispersion equations for the transverse waves (equation of the 8th algebraic degree) are splitted into two algebraic quartic equations and then solved. For a longitudinal wave, the complex amplitudes of temperature increment, translational displacements and spin–vector are coupled, unlike a transverse wave. The roots of mentioned algebraic equations are calculated by using the Wolfram Mathematica 13 symbolic computing system. The normal wavenumbers with positive real part are discriminated.
期刊介绍：
Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.
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