Nonlinear dynamics of a resonant gas sensor

Abstract

We develop a mathematical model for a resonant gas sensor made up of an microplate electrostatically actuated and attached to the end of a cantilever microbeam. The model considers the microbeam as a continuous medium, the plate as a rigid body, and the electrostatic force as a nonlinear function of the displacement and the voltage applied underneath the microplate. We derive closed-form solutions to the static and eigenvalue problems associated with the microsystem. The Galerkin method is used to discretize the distributed-parameter model and, thus, approximate it by a set of nonlinear ordinarydifferential equations that describe the microsystem dynamics. By comparing the exact solution to that associated with the reduced-order model, we show that using the first mode shape alone is sufficient to approximate the static behavior. We employ the Finite Difference Method (FDM) to discretize the orbits of motion and solve the resulting nonlinear algebraic equations for the limit cycles. The stability of these cycles is determined by combining the FDM discretization with Floquet theory. We investigate the basin of attraction of bounded motion for two cases: unforced and damped, and forced and damped systems. In order to detect the lower limit of the forcing at which homoclinic points appear, we conduct a Melnikov analysis. We show the presence of a homoclinic point for a loading case and hence entanglement of the stable and unstable manifolds and non-smoothness of the boundary of the basin of attraction of bounded motion.

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

“…If α = 0, which corresponds toL 2 = 0 while the lower microplate remains under the upper one, the system becomes a conventional microswitch with a single cantilevered microbeam. This corresponds to the microswitch studied by Nayfeh et al [23] with the pull-in voltage V p = 8.3 V, which is in agreement with Fig. 4 for α = 0.…”

“…They showed that smoothness of the boundary of the basin of attraction of bounded motions can be lost and replaced with fractal tongues as the excitation amplitude is increased. Similar results were reported by Nayfeh et al [23] for a microcantilever with a rigid plate attached to its free end.…”

“…We calculate the static response of the microsystem by solving (15) A comparison of the pull-in and pull-out voltages associated with the proposed model and that of Nayfeh et al [23] (α = 0) is shown in Fig. 7.…”

The size-dependent electromechanical instability of double-sided and paddle-type actuators in centrifugal and Casimir force fields

“…(17) in general can be specialized for each NEMS by substituting their respective formulas for f ext , M, and F . This is considered in the following subsections.…”

“…Ouakad [8] studied the e ect of shock loading on performance of a paddle-type gas sensor. More information about paddle-type NEMS is available in the literature [16,17].…”