Free vibration of a thermoelastic hollow cylinder with one relaxation time

The aim of this paper is to study the free vibration problem of a thermoelastic hollow cylinder in the context of the Lord and Shulman theory with one relaxation time. The eigenvalue approach is used to get the analytical solutions. The dispersion relations for the existence of various types of possible modes of vibrations are obtained. The validation of the roots for the dispersion relation is presented. The numerical results of frequency shift, natural frequency, and thermoelastic damping of vibrations have been presented graphically. PACS No.: 62.20.Dc. Nous etudions ici les vibrations libres d'un cylindre creux fait d'un materiau thermoelastique, en utilisant la theorie de Lord et Shulman avec un seul temps de relaxation. Nous utilisons une approche aux valeurs propres afin de trouver des solutions analytiques et obtenons les relations de dispersion pour les differents modes possibles de vibration. Nous validons les racines de ces relations de dispersion. Nous presentons graphiquement le deplacement en frequence, la frequence naturelle et l'amortissement thermoelastique des vibrations. [Traduit par la Redaction]
1. Introduction The linear theory of elasticity is of paramount importance in the stress analysis of steel, which is the most common engineering structural material. To a lesser extent, linear [...]