An exact solution for size-dependent frequencies of micro-beam resonators by considering the thermo-elastic coupling terms

Abstract

An exact solution for vibrational frequencies of micro-beam resonators is presented by using a generalized thermo-elastic model. This model is based on a combination of the non-classical continuum theory with the non-Fourier heat conduction model. The coupled governing equations and both the classical and non-classical boundary conditions of motion are based on the modified couple stress theory which can capture the size-effects in micro-scaled structures. Then, the uncoupled governing equations are obtained through mathematical operations. The exact general solutions of dimensionless deflection, rotation and thermal moments were developed for all the boundary conditions. Finally, the frequency equation is derived by imposing suitable end conditions. In this study, numerical results are obtained for micro-beam resonators with rectangular cross-sections and two types of boundary condition, i.e., clamped-isothermal, and simply supported-isothermal, which are widely used in the micro-electromechanical systems. Findings indicate that values of dimensionless frequencies are strongly dependent on the material length scale parameter and also the thermal relaxation time. Furthermore, the free-vibration behaviors predicted by the non-Fourier and Fourier heat conduction models are completely different from each other.