Response of deflection and thermal moment of Timoshenko microbeams considering modified couple stress theory and dual-phase-lag heat conduction model

Abstract

The present work focuses on the vibration analysis of Timoshenko microbeams considering the effects of the modified couple stress theory (MCST) and the dual-phase-lag (DPL) heat conduction model. The explicit expressions for equations of motion and corresponding boundary conditions of microbeam are constructed using the Hamilton’s principle and DPL heat conduction theory. For the simply supported microbeam, the deflection and thermal moment are obtained subjected to a constant impulsive force per unit length. A comparison of results between classical theory and the MCST under DPL model is specifically taken into consideration. The obtained results are also compared to the existing results for Lord-Shulman (LS) and Fourier heat conduction models. Besides, the influences of some parameters, such as the aspect ratios of length to thickness and material length-scale parameter to thickness on deflection and thermal moment of the microbeam, are analyzed in a detailed manner. The effects of phase-lag parameters associated with the DPL heat conduction model on deflection and thermal moment are also discussed. For a short time range, the present results show a good agreement with the corresponding results under LS and Fourier heat conduction models. But for a large time range, the present results show a lower rate of energy dissipation in comparison to LS and Fourier heat conduction models. In addition, the size-dependency of microbeam under the DPL model has been observed which plays an important role on the response of deflection and thermal moment. It is also revealed that there is a significant influence of phase-lags on the variation of microbeam’s deflection and thermal moment.