Nonlinear dynamic responses of electrostatically actuated microcantilevers containing internal fluid flow

Abstract

A nonlinear theoretical model for electrostatically actuated microcantilevers containing internal fluid flow is developed in the present study, which takes into account the geometric and electrostatic nonlinearities. A four-degree-of-freedom and eight-dimensional analytical modeling is presented for investigating the stability mechanism and nonlinear dynamic responses near and away from the instability boundaries of the fluid-loaded cantilevered microbeam system. Firstly, the reliability of the theoretical model is examined by comparing the present results with previous experimental and numerical results. It is found that, with the increase in flow velocity, flutter instability, pull-in instability and the combination of both can occur in this dynamical system. It is also found that the instability boundary depends on the initial conditions significantly when the internal fluid is at low flow rate. Nextly, the phase portraits and time histories of the microbeam’s oscillations and bifurcation diagrams are established to show the existence of periodic, chaotic divergence and transient periodic-like motions.