Nonlinear mechanism of pull-in and snap-through in microbeam due to asymmetric bias voltages

Pull-in and snap-through are two representative bifurcation phenomena in electrically actuated microcomponents, based on which various microdevices are designed and applied in many sensing and actuating fields. In this paper, the nonlinear mechanisms of pull-in and snap-through in a two-electrode actuated microbeam due to asymmetric bias voltages are qualitatively identified. With the considerations of midplane stretching of clamped-clamped microbeam and nonlinear electrostatic force, a continuous dynamic equation of motion is introduced after which a generalized one-degree-of-freedom (1-DOF) model derived using the differential quadrature method is deduced. By the application of the singularity theory on the static equation, transient sets are theoretically obtained which separate two-parameter space of cubic stiffness and DC voltage into seven regions. Associated bifurcation diagrams show that initially straight microbeam can exhibit snap-through motion as well as pull-in behavior when loading proper bias voltages on two electrodes. Besides, detailed division on snap-through region is numerically done and the snap-through direction is discussed and then verified. In what follows, primary resonant frequency closely related to the static solution is examined which show various attractive scenarios versus bias voltage ratio. Moreover, the method of multiple scales is utilized to derive the primary resonant response for small vibration estimation. Combined with theoretical and numerical results, dynamic snap-through motion is observed which implies that dynamic saddle-node bifurcation and interwell jumping due to energy enhancement can both increase the possibility of dynamic snap-through. During dynamic snap-through procedure, microbeam may exhibit cross-well transient chaos.