Latching in bistable electrostatically actuated curved micro beams

Abstract

Curved beams subjected to transverse force may exhibit latching phenomena, namely remain in the buckled configuration under zero force. In this study we investigate the latching in bistable electrostatically actuated initially curved and prestressed beams. The analysis is based on a reduced order (RO) model resulting from the Galerkin decomposition with buckling modes of a straight beam as base functions. Criteria for the existence of latching are derived in terms of the beam geometric parameters and axial load. Two conditions are formulated: The necessary criterion establishes the appearance of latching in the case of a symmetric snap-through, and the sufficient condition assures the existence of latching in the presence of symmetry breaking. The results provided by the RO model are compared to results obtained by direct numerical analyses. Furthermore, the dynamic behavior of curved beams prone to latching, and actuated by a suddenly applied electrostatic force of finite duration, is numerically studied. The dependence of the response on the loading parameters and the damping is presented through maps. These maps indicate the conditions required for trapping the beam at a secondary stable latching point, which is either accessible or inaccessible under quasi-static actuation. In addition, dynamic release of a latched beam is presented without the usage of an additional electrode, usually used for generating an opposite quasi-static release force.