On the effects of higher-order nonlinearities on the frequency characteristics of vibrating microbeams

There is widespread interest in the nonlinear dynamics of macro-beams and nano/micro-beams as they are essential components of structural assemblies designed for enhanced performance. A recent research effort of the authors pertains to the vibratory response of electrostatically actuated microbeams in the presence of spatially concentrated, compliant, but stiff, limit constraints. Such devices, when integrated in a microassembly, have been proposed as tunable threshold sensors for which snap-through could be induced, for example, by bursts of acceleration (e.g., Wilcox and Dankowicz [1]). The operating principle of the proposed threshold sensors is the strong destabilizing influence of lowrelative- velocity contact between the microbeam and the constraint on the vibratory steady-state response of the microbeam. Recent results have demonstrated that the onset of contact, for a sufficiently stiff constraint, results in a rapid transient from a relatively-low-amplitude solution with sustained low-velocity contact with the constraint to a relatively-high-amplitude oscillation with larger contact velocities. Indeed, by suitable design of the system parameters, this transition may result in snap-through of the microbeam towards a stationary member of opposite charge, thus shorting a circuit and triggering a suite of appropriate action. While such dynamic snap-through may occur even in the absence of a stiff constraint, the corresponding critical amplitude becomes a tunable parameter in the presence of the constraint, whereas it is determined by material and electric parameters in its absence.