Size-dependent generalized thermoelasticity model for Timoshenko micro-beams based on strain gradient and non-Fourier heat conduction theories

The governing equations of coupled thermoelasticity of Timoshenko micro-beams are developed based on the generalized thermoelastic theory and non-Fourier heat conduction model. Such problems may arise in MEMS such as micro-pumps as well as micro-sensors. The present model is on the basis of non-classical continuum theory and non-Fourier heat conduction model which has capability of capturing the size-effect in micro-scaled structures. Governing equations and both classical and non-classical boundary conditions of motion are obtained using the variational approach. As the case study, the present model is utilized for the simply supported micro-beams subjected to a constant impulsive force per unit length. It is assumed the ends of micro-beam are held at a constant temperature. Comparison of the results with those obtained by the modified couple stress and the classical continuum theories is carried out. The illustration of the existence of thermal damping in the coupled thermoelastic problem is another important contribution of this study. Findings indicate that the transient response is extremely sensitive to the material length scale parameters. In addition, only the proposed size dependent thermoelastic model can predict the unstable transient response of the micro beams under thermomechanical shocks.