Nonlinear Analysis of MEMS Electrostatic Microactuators: Primary and Secondary Resonances of the First Mode*

Abstract

We use a discretization technique that combines the differential quadrature method (DQM) and the finite difference method (FDM) for the space and time, respectively, to study the dynamic behavior of a microbeam-based electrostatic microactuator. The adopted mathematical model based on the Euler— Bernoulli beam theory accounts for the system nonlinearities due to mid-plane stretching and electrostatic force. The nonlinear algebraic system obtained by the DQM—FDM is used to investigate the limit-cycle solutions of the microactuator. The stability of these solutions is ascertained using Floquet theory and/or long-time integration. The method is applied for large excitation amplitudes and large quality factors for primary and secondary resonances of the first mode in case of hardening-type and softening-type behaviors. We show that the combined DQM—FDM technique improves convergence of the dynamic solutions. We identify primary, subharmonic, and superharmonic resonances of the microactuator. We observe the occurrence of dynamic pull-in due to subharmonic and superharmonic resonances as the excitation amplitude is increased. Simultaneous resonances of the first and higher modes are identified for large orbits in both primary and secondary resonances.

A double microbeam MEMS ohmic switch for RF-applications with low actuation voltage

“…We examine these deflections by developing closed-form solutions for the static deflections, in (15) and (16), whose coefficients are determined using the Newton-Raphson method in Mathematica from (17)- (20). The geometric and physical parameters of the microswitch are given in Table 1.…”

“…Nayfeh and coworkers [18][19][20] generated frequency and force-response curves for electrostatic microactuators whose main component is a clamped-clamped microbeam. They showed that dynamic pull-in occurs under voltages lower than the static pull-in voltage, as low as 25%, when the frequency of the AC component is in the neighborhood of a resonant frequency.…”

Dynamics of a close-loop controlled MEMS resonator

“…In fact, the electrostatic force grows and approaches infinity as the resonator displacement grows and approaches the size of the capacitor gap d → g. On the other hand, the beam stiffness k is finite, which causes the static equilibrium of the resonator to lose stability at about one-third of the gap g in a phenomenon known as static pull-in. The static and dynamic response of uncontrolled electrostatic MEMS resonators have been studied extensively by many researchers, for example Najar et al in [17,23].…”

Free and forced vibration nonlinear analysis of a microbeam using finite strain and velocity gradients theory

“…Structural elements such as beams, plates and bars have found widespread applications at the micro-and nanolevel in micro-and nanoelectromechanical systems (MEMS/NEMS) such as microactuators [5,25], piezoelectric sensors [18], mass sensors [31] and atomic force microscopes [13]. Beams are one of the most common structural elements which necessitates the study of their dynamic behavior at the microscale.…”