In this article, the wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section is discussed, using the Fourier expansion collocation method. The solid medium is assumed to be linear, isotropic, and dependent on the rate of temperature. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. By imposing the continuity conditions the frequency equation corresponding to the problem is obtained using the Fourier expansion collocation method based on Suhubi's generalized theory [Suhubi, E.S., 1975. Thermoelastic Solids. In: Eringen, A.C. (Ed.), Continuum Physics, vol. 2. Academic, New York, Chapter 2]. To compare the model with the existing literature, the results of a generalized thermoelastic solid cylinder are obtained and they are compared with the results of Erbay and Suhubi [Erbay, E.S., Suhubi, E.S., 1986. Longitudinal wavepropagationed thermoelastic cylinder. J. Thermal Stresses 9, 279-295]. It shows very good degree of agreement. The computed non-dimensional wavenumbers are presented in figures for various values of the material parameters. The general theory can be used to study any kind of cylinders with proper geometrical relations.

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The problem of wave propagation in an infinite, homogeneous, transversely isotropic polygonal cross-sectional cylinder is studied using Fourier expansion collocation method, within the framework of linearized, three dimensional theory of thermoelasticity. Three displacement potential functions are introduced, to uncouple the equations of motion and the heat conduction. The frequency equations are obtained for longitudinal and flexural (symmetric and antisymmetric) modes of vibration and are studied numerically for triangular, square, pentagonal and hexagonal cross-sectional Zinc cylinders. To study the convergence, the non-dimensional wave numbers are obtained by Fourier Expansion Collocation Method and Finite Element Method and they are compared. The computed non-dimensional wave numbers are presented in the form of dispersion curves.

The problem of wave propagation in a solid cylinder of arbitrary cross-section immersed in fluid is studied using the Fourier expansion collocation method. The frequency equations are obtained for longitudinal and flexural vibrations and are studied numerically for elliptic and cardioidal cylinders and are presented in the tabular form and also in the graphical form. The general theory can be used to study any kind of cylinder with proper geometric relations.