Crack Influences on the Static and Dynamic Characteristic of a Micro-Beam Subjected to Electro Statically Loading

Document Type : Research Paper


1 Department of Applied Mechanics, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

2 Mechanical Engineering Departments, Urmia University, Urmia, Iran


In the present work the pull-in voltage of a micro cracked cantilever beam subjected to nonlinear electrostatic pressure was studied. Two mathematical models were employed for modeling the problem: a lumped mass model and a classical beam model. The effect of crack in the lumped mass model is the reduction of the effective stiffness of the beam and in the beam model; the crack is modeled as a massless rotational spring the compliance of which is related to the crack depth. Using these two models the pull-in voltage is extracted in the static and dynamic cases. Stability analysis is also accomplished. It has been observed that the pull-in voltage decreases as the crack depth increases and also when the crack approaches the clamped support of the beam. The finding of this research can further be used as a non-destructive test procedure for detecting cracks in micro-beams.


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