Abstract
We analyze theoretically the thermal effect on the dynamics of a damped-cantilever
Timoshenko beam structure, which is featured with cross-sectional temperature gradi-
ents. 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 decom-
posing 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 high-
light the role of axial temperature gradients on the dynamic response induced by
equivalent shearing forces.
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