Nonlinear vibration analysis of a microbeam subject to electrostatic force

Chen, Xue and Meguid, S. A. (2017) Nonlinear vibration analysis of a microbeam subject to electrostatic force. Acta Mechanica, 228 (4). pp. 1343-1361. ISSN 0001-5970

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Official URL: http://dx.doi.org/10.1007/s00707-016-1777-0

Abstract

In this paper, the nonlinear vibration behavior of an electrically actuated microbeam is investigated at various levels of direct current (DC) and alternating current (AC) voltages. The governing equations are developed using Euler–Bernoulli beam theory and used to derive the frequency response of the beam. The mid-plane stretching is accounted for using von Kármán nonlinear strain, and the effects of fringing field, damping, residual axial force, and boundary conditions are also included in the model formulations. The governing equations are solved using the method of multiple scales. The results of our work reveal that the applied DC and AC voltages determine the characteristic feature of the frequency response of the microbeam. A design chart in terms of the dimensionless DC voltage and AC voltage amplitude is developed to show the domains of different characteristic frequency responses. Our results also reveal the significant effect of mid-plane stretching, damping, residual axial force, and boundary conditions on the frequency response of the microbeam. Moreover, our results further identify the effect of mid-plane stretching, damping, and residual axial force on the critical DC voltages separating the hardening and softening frequency response regions in the newly developed design chart of the micro-resonator.

Item Type: Article
Subjects: H300 Mechanical Engineering
Department: Faculties > Engineering and Environment > Mechanical and Construction Engineering
Depositing User: Becky Skoyles
Date Deposited: 12 Nov 2018 15:12
Last Modified: 12 Nov 2018 15:12
URI: http://nrl.northumbria.ac.uk/id/eprint/36627

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