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

Free vibration of an axially loaded silicon microbeam in MEMS under electrostatic actuation is studied on the basis of a sinusoidal shear deformation theory. Based on the modified couple stress theory (MCST) and von Kármán geometric nonlinearity, a nonlinear finite element formulation is derived and employed to construct the discrete nonlinear governing equations for the microbeam. The deflection of the microbeam at a given DC voltage is firstly calculated using the Newton Raphson based iterative procedure, and used to evaluate the tangent stiffness matrix. The natural frequencies of the microbeam corresponding the DC voltage are then computed. The influence of the applied voltage, the axial force as well as the material length scale parameter on the frequencies of the microbeam is studied in detail and highlighted. The dependence of the pull-in voltage upon the material length scale and the axial force is also examined and discussed.