Nonlinear mechanism of pull-in and snap-through in microbeam due to asymmetric bias voltages
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ORIGINAL PAPER
Nonlinear mechanism of pull-in and snap-through in microbeam due to asymmetric bias voltages Jianxin Han
. Lei Li . Gang Jin . Baizhou Li . Wei Wang . Qichang Zhang
Received: 15 November 2019 / Accepted: 4 August 2020 Springer Nature B.V. 2020
Abstract 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 twoelectrode 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 (1DOF) 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.
J. Han (&) G. Jin B. Li Tianjin Key Laboratory of High Speed Cutting and Precision Machining, School of Mechanical Engineering, Tianjin University of Technology and Education, Tianjin 300222, China e-mail: [email protected]; [email protected]
Keywords MEMS Singularity Transient chaos Pull-in Snap-through Multiple scales
L. Li School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049, China
1 Introduction
W. Wang Q. Zhang Tianjin Key Laboratory of Nonlinear Dynamics and Control, School of Mechanical Engineering, Tianjin University, Tianjin 300350, China
With rapid development of micro-nano-manufacturing and high technical demand, micro-electromechanical systems (MEMSs), due to their advantages of
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geometric simplicity and broad applicability, have gathered tremendous attentions and developed rapidly in sensing, actuating and filtering fields.
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