Vibration analysis of transversely isotropic hollow cylinder considering three different theories using the matrix Frobenius method

Purpose The purpose of this paper is to deal with the three-dimensional analysis of free vibrations in a stress-free and rigidly fixed homogeneous transversely isotropic hollow cylinder in the context of three-phase-lag (TPL) model of hyperbolic thermoelasticity. Design/methodology/approach The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. Findings The natural frequency, dissipation factor and inverse quality factor in the stress-free and rigidly fixed hollow cylinder get significantly affected due to thermal vibrations and thermo-mechanical coupling. Originality/value The modified Bessel functions and matrix Frobenius method have been directly used to study the vibration model of a homogeneous, transversely isotropic hollow cylinder in the context of TPL model based on three-dimensional thermoelasticity.