Nonlinear Dynamic Analysis of an Electrostatically Actuated Cylindrical Micro-Beam Subjected to Cross Fluid Flow

Abstract

This work investigates the nonlinear dynamic behavior of an electrostatically actuated clamped–clamped cylindrical micro-beam subjected to vortex induced vibrations (VIV). Lift and drag forces are the two basic flow-induced factors affecting the dynamics of the micro-beam under fluid flow which are neglected in micro-structures immersed in stationary fluids. The electrostatically actuated micro-beam is modelled using Timoshenko beam theory and the impact of the fluid cross-flow is accounted for by considering its resultant force elements comprising inertia, lift and drag force vectors. In addition, the size dependency effect on the nonlinear dynamics of the micro-beam is studied based on the Modified Couple Stress Theory (MCST). The governing nonlinear equations are solved using the Galerkin and step-by-step linearization method to evaluate the response of the coupled structure to a combined voltage excitation plus fluid flow. Response of the micro-beam to different input voltages in the presence of fluid velocities are investigated and it is shown that the range and intensity of the lock-in regime is effectively controlled by the input voltage and fluid-to-beam density ratio.