REDUCED-ORDER MODELS OF ELECTROSTATICALLY ACTUATED FLEXIBLE MEMS STRUCTURES SUFFERING IMPACTS

The engineering of man-made devices aimed at purposely exploiting desirable nonlinearities may enhance the performance characteristics in existing applications by orders of magnitude. Examples of such efforts are switching controllers [1] that rely on corner-collision bifurcations in piecewise-smooth systems for nonlinear stabilization of limit cycles in smooth systems; micro-oscillator mass sensors [2,3] designed to exhibit hardening parametric resonance curves and to trigger near smooth fold bifurcations. The present work moves towards the exploitation of non--persistent, discontinuity-induced bifurcation scenarios in vibro-impacting systems as a nonlinear phenomenon in device design. The emphasis is on sudden changes in system transient and steady-state response following the onset of low-relative-velocity, grazing mechanical contact. The engineering objective is to explore the practical use of such changes as signatures of the crossing of a system parameter of a predetermined threshold value in limit-switch design. Limit-switch sensors of this kind are examples of so-called bifurcation amplifiers. As the control parameter exceeds the critical value, there is an associated loss of stability or disappearance of the original steady-state behavior resulting in a rapid transition to a different steady-state attractor. Examples of such bifurcations, such as fold and subcritical pitchfork bifurcations of equilibria, are exploited in previously documented limit-switch devices. Prior work of the authors on lumped-mass, vibro-impacting systems has investigated some properties of threshold switches based on grazing-induced instabilities, including transient growth rates that far exceed those of their smooth counterparts as well as detectable changes in amplitude and frequency content [4--6]. The design of such a limit switch in actual MEMS flexible structures becomes feasible provided that there are reliable predictive dynamical models that well describe the response of the MEMS structures to the onset of mechanical contact.