Electro-dynamic behavior of an electrically actuated micro-beam: Effects of initial curvature and nonlinear deformation

This paper presents a curved beam model for the nonlinear electro-dynamic analysis of micro-beams with initial curvature, taking into account the nonlinear electric force and nonlinear deformation. The governing equations of motion and boundary conditions are derived in an arc coordinate system. Unlike previous studies based on von Karman nonlinearity or considering mid-plane stretching only, the present study does not involve any assumptions on nonlinear deformation. Differential quadrature method and Petzold–Gear BDF method are employed to obtain the nonlinear electro-dynamic behavior of curved micro-beams. The effects of nonlinear deformation, initial gap and initial rise on the nonlinear electro-dynamic characteristics are studied.

► A new nonlinear curved micro-beam model without assumption is proposed. ► Nonlinear equations of motion for electrically actuated micro-beams are established. ► Nonlinear electro-dynamic characteristics are numerically obtained and presented. ► Dynamic pull-in voltage and collapse mode of curved micro-beams are obtained. ► Nonlinear dynamic deflection, fundamental frequency and phase portrait are studied.