An Exact Solution for Classic Coupled Generalized Thermoviscoelasticity in Cylindrical Coordinates

In this paper, the classic coupled Generalized thermo-viscoelasticity model of hollow and solid cylinders under radial symmetric loading condition (r, t) is considered. A full analytical method is used, and an exact unique solution which is the most complete type solution of the classic coupled generalized thermo-viscoelasticity equations is presented heretofore. The method of solution is based on the Fourier’s expansion and Eigen- function methods, which are traditional and routine methods in solving the partial differential equations. The thermal and mechanical boundary conditions, the body force, and the heat source are considered in the most general forms and where no limiting assumption is used. The Kelvin-Voigt model at problem of magneto-thermo-viscoelasticity has extensive uses. This theory uses in divers fields, such as geophysics for understanding the effect of the Earth`s magnetic field on seismic wave, damping of acoustic waves in a magnetic field, development of a highly sensitive superconducting magnetometer, electrical power engineering, optics, supersonic airplanes. At the end, numerical results are presented and compared with classic theory of thermoelasticity.