Individual and combined static stabilities in electrostatically actuated initially curved coupled micro beams

Abstract

A stability study of electrostatically actuated micro-meta-structure (MMS), composed of two double clamped, initially curved micro beams and coupled via a rigid truss at their respective centres, is studied via a reduced order (RO) model. The study is based on the energy method and Lyapunov stability analyses, carried out in conjunction with the implicit arc-length “Riks” continuation method, to characterise the stability properties of several key configurations. By sweeping through each of the configurations, we show that it is possible to ascertain the stability of each beam individually, as well as of the entire structure, globally. The analysis has brought forth interesting characteristics, hitherto unknown, which complement any static analysis, by foretelling locations at which the MMS loses stability, causing a shift in limit point locations. It is shown that due to stability mismatch between the two beams, tristable properties, which could be present in one of them, will be nullified due to instability present in the other one. The Lyapunov analysis further discloses the location of a new equilibrium branch, located at an offset from the predicted equilibrium curve. The study begins with an analysis of the structure under displacement-independent “mechanical” load to facilitate its understanding, while allowing validation of the RO model against a finite element (FE) model, thus laying a foundation for the electrostatic loading analysis. It is concluded that a metastructure, composed of two sub-structures, is stable if an only if (iff) the two sub-structures are stable. Otherwise, new equilibrium branches will present themselves when conducting an experimental quasi-static loading. The study also shows that as far as stability analysis and quasi-static loadings are concerned, the newly formalised dynamic RO model bears merit.