Vibration of a Thermoelastic Microbeam due to the Thermoelectrical Effect of a Strip of Graphene

In this work, an analysis of thermoelastic, homogeneous, and isotropic microbeams was conducted in the context of the non-Fourier heat conduction law. The first end of the microbeam was based on a graphene strip, which was connected to an electrical voltage source. Under simple boundary conditions maintained by fixed side ratios, the Lord–Shulman model of generalized thermoelasticity was applied. The microbeam was thermally loaded with a heat source due to the thermal effect of the electrical current that ran through the strip of graphene. Laplace transformation of the time variable was utilized to solve controlled differential equations. All the solutions were found in the Laplace transform domain. Tzou's approximation approach, which relies on an iteration formula, was used to numerically calculate the Laplace transform inversions. For different values of the electrical voltage and the resistance of the graphene strip, different graphs were used to show the numerical results. The electrical voltage and the electrical resistance were reported to have significant influences on all the studied functions of the microbeam. Thus, controlling a microbeam’s vibration and energy could be accomplished by tuning the electrical resistance and applied voltage.