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Abstract
The three-dimensional free vibrations in a simply supported homogeneous isotropic, thermally conducting, circular cylinder of finite length with an eccentrically located inner circular cavity have been studied. The surfaces of the cylinder are subjected to stress free and thermally insulated or isothermal boundary conditions. The three-dimensional linear theory of coupled thermoelasticity has been employed to model the problem. The displacement potential functions have been introduced to decouple purely shear and longitudinal motions. The purely transverse wave has been found to remain unaffected due to thermal field. The translation addition theorem for cylindrical wave functions along with orthogonal series expansions has been used to develop the exact solution. To illustrate the analytical results, the numerical solution of some relations and equations have been obtained to compute lowest frequency and dissipation factor versus eccentricities, for selected length to radius ratio and radius ratio of hollow cylinder. The computer simulated results have been carried out with the help of MATLAB software and are presented graphically.