Nonlinear oscillation of a microbeam due to an electric actuation—Comparison of approximate models

• Published in: Zeitschrift für angewandte Mathematik und Mechanik Vol. 104; no. 2
• Main Authors: Andrianov, Igor V., Awrejcewicz, Jan, Koblik, Steve G., Starushenko, Galina A.
• Format: Journal Article
• Language: English
• Published: Weinheim Wiley Subscription Services, Inc 01.02.2024
• Subjects: Actuation; Geometric nonlinearity; MacLaurin series; Microbeams; Nonlinear differential equations; Oscillations
• ISSN: 0044-2267; 1521-4001
• DOI: 10.1002/zamm.202300091

In this paper, oscillations of the electrically actuated microbeam are considered, described by strongly nonlinear differential equations. One of the essentially nonlinear effects is the pull‐in phenomenon, that is, the transition of the oscillatory regime to the attraction regime. This effect is considered in the paper on the basis of various approximate models. In particular, the error of replacing the original nonlinearity by its expansion in the Maclaurin series is estimated. It is shown that such an approximation can only be used for voltage values that are far from critical. Estimates are also given for initial displacements and velocities, which guarantee an oscillating character of solutions. The electrically activated oscillations of the microbeam are considered taking into account the geometric nonlinearity within the framework of the Kirchhoff model. The dependence of pull‐in value on geometric nonlinearity is investigated. In this paper, oscillations of the electrically actuated microbeam are considered, described by strongly nonlinear differential equations. One of the essentially nonlinear effects is the pull‐in phenomenon, that is, the transition of the oscillatory regime to the attraction regime. This effect is considered in the paper on the basis of various approximate models. In particular, the error of replacing the original nonlinearity by its expansion in the Maclaurin series is estimated. It is shown that such an approximation can only be used for voltage values that are far from critical.…