Within the framework of the theories of coupled linear thermoelasticity and Timoshenko beams, the vibration and thermoelastic damping (with emphasis on the transverse ones) of circular cross-section beams are studied. The governing equations are derived for the case of general mechanical boundary conditions and special thermal boundary conditions that follow the Newton surface heat transfer law. A variational principle governing the eigenfunctions associated with an eigenvalue is formulated. An exact solution, together with the thermoelastic damping coefficient, is obtained for the case of transverse vibrations of a simply supported beam with lateral surfaces thermally insulated and end surfaces kept at constant temperature. Numerical results, together with the discussion for the first two eigenvalues and the thermoelastic damping coefficients, are also presented.

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