Vibration response of Timoshenko perforated microbeams under accelerating load and thermal environment

Abstract

This article presents a dynamic finite elements procedure capable of analyzing the dynamic behavior of perforated Timoshenko microbeams in thermal environment and subjected to moving mass for the first time. An analytical geometrical model is presented to incorporate the perforation effect into the governing equations. The microstructure size dependent effect is incorporated based on the modified couple stress theory. Based on the presented geometrical model, the dynamic equations of motion including the interaction terms of the mass inertia are derived from the exact differential of the displacement functions of the beam relative to the mass contact point. To investigate the temperature effect on the dynamic behavior, thermal loading with different temperature rise profiles are considered. Thermal stresses, due to thermal loads are converted to mechanical stresses and then the thermal rigidity matrix is combined with the stiffness matrix of the beam. The dynamic finite element equations of motion are derived including the thermal effect. The system equations are solved numerically by using implicit time integration method due to its stability. The proposed numerical procedure is checked by comparing the obtained results with the available solutions and good agreement is observed. Effects of perforation parameters, thermal loading profile, moving mass characteristics, as well as the moving speed on the dynamic behavior of perforated microbeams are studied. The obtained results are helpful in the design and manufacturing of perforated microbeams structural systems.