Three-dimensional vibration analysis in transversely isotropic cylinder with matrix Frobenius method

摘要

This article deals with the study of three-dimensional vibrations in stress free as well as rigidly fixed, thermally insulated (or isothermal), homogeneous transversely isotropic solid cylinder under the purview of three-phase lag model of generalized thermoelasticity. The displacement potential functions have been introduced in the equations of motion and heat conduction in order to decouple the purely shear and longitudinal motions. The matrix Frobenius method of extended power series is employed to obtain the solution of coupled ordinary differential equations along the radial coordinate. Circumferential wave propagation in cylindrical curved plate is discussed. To illustrate the analytic results, the numerical solution of various relations and equations have been carried out to compute the lowest frequency, inverse quality factor, and dissipation factor of vibrations and the computer-simulated results are presented graphically for different thermoelastic models.