Exact solution for thermal damping of functionally graded Timoshenko microbeams

This article deals with the thermoelastic damping problem in a functionally graded (FG) Timoshenko microbeam. Thermal and mechanical properties of the microbeam vary in the thickness direction according to the power lawrelation. Employing Timoshenko beam theory, the governing dynamic equation coupled with thermal effects of the FG microbeam is developed. Afterwards, Using the Taylor series expansion for material properties, the heat conduction equation is solved analytically for temperature in the form of a power series. The free vibration of the FG microbeam is analyzed to achieve the natural frequencies and thermal damping ratio of the FG microbeam. The effect of FG index on the thermoelastic damping ratio is investigated in different aspect ratios. Also comparison studies are made between the results obtained from the models based on the Euler-Bernoulli and Timoshenko beam theories.