Analytical analysis of the thermal effect on vibrations of a damped Timoshenko beam

• Thermal effect on the damped-Timoshenko-beam dynamics is studied theoretically.
• Uneven-temperature-induced forces and temperature-dependent modulus are considered.
• Analytical solutions of vibrations are given with thermal factors incorporated.
• Thermal eigenvalue is as critical as temperature gradient in thermal vibrations.
• Axial temperature variations are important in predicting thermal vibrations.

We analyze theoretically the thermal effect on the dynamics of a damped-cantilever Timoshenko beam structure, which is featured with cross-sectional temperature gradients. The thermal effect is incorporated in the dynamic model via the temperature-dependent elastic modulus and the temperature-gradient-induced thermal force. The inhomogeneous boundaries introduced by the thermal moment are handled by decomposing the total displacement into static and dynamic displacements. In the end, numerical results based on the analytical solutions are given for a better understanding of the thermal effect on the dynamic behaviors. The solutions reveal the circumstances in which thermal eigenvalues should be considered together with the cross-sectional temperature gradients in predicting thermal vibrations. Moreover, the results also highlight the role of axial temperature gradients on the dynamic response induced by equivalent shearing forces.