The Influence of Higher-Order Mode Shapes for Reduced-Order Models of Electrostatically Actuated Microbeams

Reduced-order models for micro-electromechanical structures possess several attractive features when compared with computational approaches using, e.g., finite-element packages. However, also within the business of reduced-order modeling, there are different approaches that yield different results. The efficiency of such approaches has to be judged according to, first, the purposes and aims of the model and, second, according to computational expenses and modeling efforts. This paper deals specifically with the frequently asked question of how many modes have to be considered in the discretization procedure to ensure an efficient reduced-order model. A consistent nonlinear continuum model is employed to describe a doubly clamped microbeam subject to two cases of electromechanical actuation. The analysis, confined to the static behavior, concentrates on two discretization techniques and addresses the differences between the final reduced-order models, accordingly. The results show significant differences with respect to the number of implemented linear-undamped mode shape functions, which are used as basis functions in the approximation procedure. This is demonstrated for the two mentioned distinct excitation schemes of the doubly clamped microbeam. The purposes of this paper are twofold. First, it draws attention to the differences between reduced-order models, which have been discretized one way or the other according to investigation goals and purposes. Second, it serves as a guideline for future micro- and nano-electromechanical system modeling by elaborating the advantages and disadvantages of both techniques.