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Bistable microstructures under electrostatic loading

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Bistable micro devices are distinguished by their ability to stay in two different configurations at the same loading. Micro- and nanoelectromechanical systems (MEMS/NEMS) incorporating bistable elements are advantageous in a variety of applications ranging from electrical and optical switches, variable capacitors and up to non-volatile memories and logical elements. Behaviour of bistable structures under conventional mechanical loading is a well-established topic in structural mechanics. However, the presence of nonlinear electrostatic forces is abundant in MEMS /NEMS, affecting the stability of the structures, and leading to new phenomena not encountered in conventional large-scale structures. In the present work, incorporating both theoretical and experimental procedures, two types of bistable structures are considered, initially curved clamped beams and imperfect circular plates (shallow caps). The beam is described by nonlinear Kirchhoff model, while the plate is modelled using Föppl von-Kármán, and Berger theories. The analyses are based on reduced order (RO) models resulting from Galerkin’s decomposition with buckling modes of a straight beam, or flat plate, used as the base functions. Criteria of a symmetric limit point buckling, non-symmetric bifurcation and latching are developed in terms of the geometric parameters of the structures and initial pre-stress. The RO model results are validated using nonlinear finite elements and finite differences analyses carried out in conjunction with the “Riks” arc-length continuation method. The results also indicate that reasonably low voltages can actuate micro plates having realistic dimensions, suggesting the suitability of such elements in various applications. Experimental results are found to be consistent with the beams buckling criteria, predicted numerically as well as by the RO models. Theoretical and experimental results collectively indicate that the nonlinearity of the electrostatic loading has major influence on the structures behaviour. Both snap-through instability and symmetry breaking occur at lower voltages and smaller displacement when compared to the case of a purely “mechanical” load. Moreover, electrostatic forces result in appearance of additional pull-in instabilities. The study is also extended to examine the effects of dynamic actuation on micro beams. Among such actuations stand two in particular, namely dynamic snap-through to a statically inaccessible stable equilibrium (dubbed as dynamic trapping), and a dynamic release effect of a latched beam. For both cases, corresponding experiments were carried out, demonstrating both phenomena.

This talk is part of the Engineering Department Dynamics and Vibration Tea Time Talks series.

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