Vibration of electrically actuated mems Timoshenko microbeams based on a hierarchical beam element

In this paper, vibration of Timoshenko microbeams with an axial force in microelectromechanical systems (MEMS) is studied for the first time by using a nonlinear finite element procedure. Based on the von Karm´ an geometric nonlinearity and the modified couple stress theory (MCST), a beam element is formulated by employing hierarchical functions to interpolate the displacement field.