Thermoelastic vibration of Timoshenko beam under the modified couple stress theory and the Moore–Gibson–Thompson heat conduction model

Abstract

In modeling of micro/nanodevices, numerous approaches have been developed that take into account material length scale parameters to capture size effects. In this work, the variational formulation of the microstructure-dependent Timoshenko beam model is developed considering Hamilton’s principle and modified couple stress theory (MCST) which involves the material length scale parameter. The Moore–Gibson–Thompson (MGT) thermoelastic model is employed to present the governing equations of motion and boundary conditions. The numerical outcomes illustrated by classical and non-classical approaches reveal the behavior of both the deflection and thermal moment of the beam. In addition, the dissipation in the deflection and the thermal moment is visually depicted in standardized curves. Several peaks in graphical plots are then detected as a function of the dimensionless time, which bring to light some interesting features of MGT model in the prediction of thermoelastic vibration of the microstructure model of Timoshenko beam.