crack influences on the static and dynamic characteristic of a micro-beam subjected to electro statically loading

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.