Abstract
A generalized transverse wave is a propagating acceleration discontinuity on which the temperature and the entropy, together with their gradients, are continuous. In a heat-conducting elastic material the propagation and growth of such waves are uninfluenced by thermomechanical interaction. It is shown in this paper that in any given plane there is at least one direction in which a generalized transverse wave may propagate, and the existence is also proved of at least one direction in which a pair of generalized transverse waves may travel. Necessary and sufficient conditions are established for the speeds of propagation of these waves to be real. Relationships between transverse and generalized transverse waves are also studied, and in the last two sections of the paper the directions in which generalized transverse waves may propagate in an isotropic heat-conducting elastic material are systematically worked out and classified.
Résumé
Une onde transversale generalisée est une discontinuité d'acceleration en train de se propager sur laquelle la température, l'entropie ainsi que leurs dérivées sont continues. La propagation et le développement de telles ondes dans des matiéres conductrices de chaleur, ne sont pas affectés par interaction thermo-mécanique. On démontre qu'il existe au moins une direction dans tout plan donné dans laquelle une onde transversale generalisée peut se propager, et on prouve aussi qu'il existe au moins une direction dans laquelle une paire d'ondes transversales generalisées peuvent se propager. On détermine quelles sont les conditions nécessaires et suffisantes pour que les vitesses de propagation soient réeles. Les relations entre les ondes transversales et transversales generalisées sont aussi étudiées, et dans les deux dernières sections on obtient et classifie systematiquement les directions dans lesquelles les ondes transversales generalisées peuvent se propager dans une matière élastique, isotropique, conductrice de chaleur.
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Chadwick, P., Currie, P.K. On the propagation of generalized transverse waves in heat-conducting elastic materials. J Elasticity 4, 301–315 (1974). https://doi.org/10.1007/BF00048613
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DOI: https://doi.org/10.1007/BF00048613