0
Research Papers

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

[+] Author and Article Information
Stefanie Gutschmidt

Department of Mechanical Engineering, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealandstefanie.gutschmidt@canterbury.ac.nz

J. Appl. Mech 77(4), 041007 (Apr 09, 2010) (6 pages) doi:10.1115/1.4000911 History: Received February 12, 2009; Revised October 16, 2009; Published April 09, 2010

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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Definition sketch of the clamped-clamped microbeam system for the one-sided electrode configuration

Grahic Jump Location
Figure 6

(a) The influence of the number of symmetric modes retained in GM 13 on the variation of w(s) with Vdc; (b) zoom in of (a); bold lines: stable and thin lines: unstable

Grahic Jump Location
Figure 2

The influence of the number of symmetric modes retained in the MWR on the variation of w(s) with Vdc; compare also with Fig. 3 in Ref. 4; bold lines: stable and thin lines: unstable

Grahic Jump Location
Figure 3

(a) The influence of the number of symmetric modes retained in the GM on the variation of w(s) with Vdc; (b) zoom in of (a); bold lines: stable and thin lines: unstable

Grahic Jump Location
Figure 4

Comparison between three-mode MWR approximation 14and one-mode GM approximation 12; bold lines: stable and thin lines: unstable

Grahic Jump Location
Figure 5

(a) The influence of the number of symmetric modes retained in MWR 20 on the variation of w(s) with Vdc; (b) zoom in of (a); bold lines: stable and thin lines: unstable

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In