Effects of Phase Lags on Thermoelastic Damping in Micro-Beam Resonators

The aim of the present paper is to study the thermoelastic damping of a micro-beam resonator in the context of the generalized thermoelasticity theory with three-phase-lag (TPL). The thermoelastic damping of the micro-beam resonator is obtained by the Laplace transform procedure as well as by the finite-sine Fourier transformation. The vibration responses of deflection and thermal moment are obtained for the micro-beams with simply supported and isothermal ends. Initially, the analytic solution is obtained for the amplitudes of deflection and thermal moment. It was observed that both amplitudes are attenuated and the vibration frequency is increased with the three-phase-lag. The effects of phase-lags on the deflection and thermal moment are obtained and evaluated by comparing the present numerical results with the corresponding results based on the theory of thermoelasticity of type GN-III. It was observed that higher values of deflection and thermal moment of the resonator are obtained for the TPL when compared with those of the GN-III model. It was also found that these properties are size-dependent.