Abstract
Microelectromechanical switch has become an essential component in a wide variety of applications, ranging from biomechanics and aerospace engineering to consumer electronics. Electrostatically actuated microbeams and microplates are chief parts of many MEMS instruments. In this study, the nonlinear characteristics of coupled longitudinal–transversal vibration are analyzed, while an electrostatically actuated microbeam is designed considering that the frequency ratio is two to one between the first longitudinal vibration and transversal vibration. The nonlinear governing equations are truncated into a set of coupled ordinary differential equations by the Galerkin method. Then the equations are solved using the multiple-scales method and the nonlinear dynamics of the internal resonance is investigated. The influence of bias voltage, longitudinal excitation and frequency detuning parameters are mainly analyzed. Results show that using the pseudo-arclength continuation method, the nonlinear amplitude–response curves can be plotted continuously. The saturation and jump phenomena are greatly affected by the bias voltage and the detuning frequency. Beyond the critical excitation amplitude, the response energy will transfer from the longitudinal motion to the transversal motion, even the excitation is employed on the longitudinal direction. The large-amplitude jump of the low-order vibration mode can be used to detect the variation of the conditions or parameters, which shows great potential in improving precision of MEMS switches.
Highlights
Electrostatic actuation is the most popular actuation mechanism used in microelectromechanical systems (MEMS) [1,2]
Wang [31] presented a size-dependent model for electrostatically actuated microbeam-based MEMS using strain gradient elasticity theory, in the study the relation of the geometry size and the normalized pull-in voltage were analyzed in detail
To extend the application of bifurcations of the coupling longitudinal–transversal vibration in the design of MEMS switches, this paper mainly focused on the nonlinear characteristics of an electrostatically actuated microbeam, and the coupled longitudinal–transversal vibration was analyzed in detail
Summary
Electrostatic actuation is the most popular actuation mechanism used in microelectromechanical systems (MEMS) [1,2]. Younis [26,27] used analytical approaches to investigate the behavior of electrically actuated microbeam-based MEMS, and proposed a reduced-order model in nonlinear dynamic analysis of MEMS. Wang [31] presented a size-dependent model for electrostatically actuated microbeam-based MEMS using strain gradient elasticity theory, in the study the relation of the geometry size and the normalized pull-in voltage were analyzed in detail. Ghayesh [33] investigated the nonlinear size-dependent behavior of an electrically actuated MEMS resonator based on the modified couple stress theory and a high-dimensional reduced-order model. Li [40] used the modified couple stress-based strain gradient theory to construct a unified nonlinear model for an electrostatic MEMS microbeam capacitive switch, the quasistatic and dynamic behavior of which were studied systematically.
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