Effect of phase-lag on thermoelastic vibration of Timoshenko beam

Abstract

An explicit formula of coupled three-phase-lag (TPL) thermoelasticity theory under the Timoshenko beam is constructed for microbeam resonators. The constructed mathematical model is based on the modified couple stress theory which implies a prediction of size-dependent effects in microbeam resonators. By using Hamilton’s principle, governing equations for motion and boundary conditions are derived. The thermal moment and thermal deflection of microbeam resonators are studied analytically and numerically. A comparison of the results between modified coupled stress theory and classical theory is executed for TPL, GN-II, and Lord–Shulman (LS) models. Also, a comparison of the results between TPL, GN-II, and LS models for modified coupled stress theory is done. Besides, the result is presented for silicon microbeam for different aspect ratios and phase-lags. It demonstrated the result corresponding to the behavior of thermoelastic frequencies of microbeam resonators.