Size-dependent dynamic pull-in instability of vibrating electrically actuated microbeams based on the strain gradient elasticity theory

This paper presents the impact of vibrational amplitude on the dynamic pull-in instability and fundamental frequency of actuated microbeams by introducing the second order frequency–amplitude relationship. The nonlinear governing equation of microbeam predeformed by an electric force including the f...

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Bibliographic Details
Published in:Acta astronautica 2014-02, Vol.95, p.111-123
Main Author: Sedighi, Hamid M.
Format: Article
Language:English
Subjects:
Dynamic pull-in instability
Elasticity
Frequency–amplitude relationship
Instability
Mathematical analysis
Microbeam vibration
Microbeams
Microstructure
Nonlinear dynamics
Parameter Expansion Method
Size-dependent
Stability
Strain
Strain gradient elasticity theory
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Summary:This paper presents the impact of vibrational amplitude on the dynamic pull-in instability and fundamental frequency of actuated microbeams by introducing the second order frequency–amplitude relationship. The nonlinear governing equation of microbeam predeformed by an electric force including the fringing field effect, based on the strain gradient elasticity theory is considered. The predicted results of the strain gradient elasticity theory are compared with the outcomes that arise from the classical and modified couple stress theory. The influences of basic nondimensional parameters on the pull-in instability as well as the natural frequency are investigated by a powerful asymptotic approach namely the Parameter Expansion Method (PEM). It is demonstrated that two terms in series expansions are sufficient to produce an acceptable solution of the microstructure. The phase portrait of the microstructure shows that by increasing the actuation voltage parameter, the stable center point loses its stability and coalesces with unstable saddle node. •The governing equation of microbeams based on the strain gradient elasticity theory is considered.•Size-dependent pull-in instability of microbeams is investigated.•The impact of vibrational amplitude on microbeams pull-in instability is studied.•The second-order frequency–amplitude relationship of microbeams vibration is presented.•The influences of significant parameters on the dynamic pull-in voltage are investigated.
ISSN:0094-5765
1879-2030
DOI:10.1016/j.actaastro.2013.10.020