Nonlinear Dynamic Analysis of Cracked Micro-Beams Below and at the Onset of Dynamic Pull-In Instability

Journal of Solid Mechanics

مقاله 8، دوره 10، شماره 1، خرداد 2018، صفحه 110-123   

نوع مقاله: Research Paper

نویسندگان

R Hassannejad^* ؛ Sh Amiri Jahed

Department of Mechanical Engineering, University of Tabriz, Tabriz, Iran

چکیده

In this paper, the effect of the crack on dynamic behavior of cracked micro-beam in the presence of DC and AC loads are investigated. By applying the residual axial stress and fringing field stress, a nonlinear analytical model of cracked micro-beam is presented and crack is modeled by a massless rotational spring. The governing equation of the system is solved using Galerkin procedure and shooting method. The equilibria curve and dynamic response of cracked cantilever and clamped-clamped micro-beam are extracted below and at the onset of the dynamic pull-in instability. The results show that the behavior of cracked micro-beam is different from ordinary cracked beam due to nonlinear effects. For a fixed relative crack location, increasing the crack depth causes increasing in the resonance amplitude and reduction in the resonance frequency below dynamic pull-in instability. Also, in cracked cantilever micro-beams, by approaching the crack to fixed end, the resonance frequency reduces and the resonance amplitude increases. In cracked clamped-clamped micro-beam, trend of variations of resonance frequency and resonance amplitude against the crack location is not regular. At the onset pull-in instability, the presence of the crack causes cyclic-fold bifurcation points to appear at the lower frequency. Therefore, it causes early pull-in phenomenon or unwanted abrupt change at the micro-beam behavior. The achievement of this study is simulation of the response of the faulty low-voltage switch and MEMS resonators for different severity of crack at the onset of dynamic pull-in phenomenon.  

کلیدواژه‌ها

Micro-electromechanical systems؛ Crack؛ Pull-in phenomenon؛ Nonlinear dynamics؛ Bellow and at the onset of pull-in instability

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