Analysis of thermoelastic damping of functionally graded material beam resonators

In this paper, thermoelastic damping (TED) in free vibrating functionally graded material (FGM) micro beams with rectangular cross sections is investigated. The material properties of the micro beams are assumed to be varied continuously in the thickness direction. Based on the classical beam theory and coupled thermo-elastic dynamics, governing equations coupled with the thermal effects derived in terms of the deflection and temperature rise filed. A layer-wise homogenization method is proposed to solve the one-way coupled heat conduction equation with variable coefficients. By using the mathematical similarity between the vibration equation of the FGM beam and that of the reference homogenous beam, complex frequency of the FGM beam including TED is expressed in the terms of that of the reference homogenous beam without TED. Numerical results of TED are obtained for the specific material constituents and the power law gradient profile. The effects of the material gradient index, beam thickness, vibration modes and boundary conditions on the TED of the FGM micro beams are studied in detail.