The influence of higher in- and out-of-plane natural modes on dynamic pull-in instability of electrically actuated micro-plates

Generating reduced-order models (ROMs) is one of the most efficient procedures for predicting pull-in instability threshold in electrically actuated rectangular micro-plates. To date, there exist some different approaches for this procedure in the literature with different numbers of employed natural modes which yield different results. The main objective of the present paper is to answer the basilar question of how many natural modes for discretising the in- and out-of-plane displacements should be included to ensure an efficient ROM. To this end, a full geometric non-linear Kirchhoff’s plate model with fully clamped boundary conditions, which accounts for both in-plane and transverse displacements is considered. A multi-mode ROM is also developed and both static and dynamic instability thresholds of the system are extracted. Convergence studies on both static and dynamic findings are also performed to illustrate the importance of each in- or out-of-plane mode on the accuracy of the results. Utilising the present convergence studies, the minimum number of in- and out-of-plane modes, which should be employed to achieve precise predictions, is determined. At the rest of the paper, effect of micro-plate inertia on reducing the instability threshold of systems with different initial gaps and aspects ratios is also studied in details.