Free vibration of axially loaded microbeam in MEMS based on sinusoidal shear deformation theory

Free vibration of a silicon microbeam in micro-electromechanical systems (MEMS) subjected to electrostatic and axial forces is studied in the framework of a sinusoidal shear deformation theory. A nonlinear finite element formulation based on the von Kármán nonlinear assumption and the modified couple stress theory (MCST) is formulated and employed to establish the discrete nonlinear governing equations for the microbeam. The deflection of the microbeam at a given direct current (DC) voltage is firstly calculated by the Newton Raphson method and used to evaluate the natural frequencies. The influence of the applied voltage and the microsize effect on the frequencies is investigated in detail. The results reveal that the microstructural parameter has an important role in the vibration the microbeam, and the natural frequencies are underestimated by ignoring the microstructural parameter. The dependence of the pull-in voltage upon the material length microscale and the axial force is also examined and discussed. © 2023, Publishing House of Natural Science and Technology, VAST. All rights reserved.