Near-grazing, low-velocity contact in vibro-impacting systems has been shown to result in dramatic changes in steady-state system response following rapid transient growth of deviations away from the pre-grazing steady-state response. In low-dimensional example systems such transitions are often associated with large jumps in response amplitude. Coupled with the rapidity of the transient dynamics, this phenomenology supports the design of limit-switch sensors that trigger at the onset of grazing contact. A particularly exciting area of application of such sensors, and one in which their implementation might offer particular advantages, is in the context of microelectromechanical structures. Here, desirable scaling effects, such as increased system frequencies, low damping, batch fabrication, and decreased packaging size, can be leveraged. Fabricating simple beam structures at the microscale is relatively easier than fabricating proof-mass-based lumped-parameter systems with elaborate suspension structures. Consequently, it often becomes necessary to account for the flexibility of participating mechanical members, for example doubly-clamped, silicon-based beam elements. Physical contact further poses modeling challenges, as the flexibility of the beam elements and that of the contact region necessitate a compliant, but very stiff model description. The present work investigates a sequence of reduced-order models for such a doubly-clamped beam, subject to capacitive electrostatic actuation and a low-compliance physical constraint localized at a point along the span of the beam. The objective is to determine whether grazing-induced transitions, characteristic of lumped-mass models, are retained in the flexible structure. Specifically, numerical simulations are employed to quantify the variations in the response amplitude following the onset of contact and to contrast these to a spreading of system energy across mechanical modes.

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