Dynamic Behavior of a Micro-Beam Subjected to Voltage and Fluid Flow as a Micro Vortex Generator

The present work investigates the nonlinear vibration of a cantilever cylindrical micro-beam subjected to voltage and fluid flow as a micro vortex generator. As the microbeam is subjected to the fluid with given velocity, in addition to the load due to fluid added mass, the lift and drag forces as the two basic flow-induced factors affecting the dynamics of the micro-beam are modelled using the Van der pol equation. The Euler-Bernoulli beam theory is used to model the cross fluid motion of the beam under nonlinear electrostatic force as result of applied voltage. The Galerkin method is used to convert the partial differential equation to regular differential equations as well as to solve the coupled nonlinear equations governing the micro-beam motion and the wake oscillation to evaluate the response of the coupled structure to a combined applied voltage and fluid flow. The effect of fluid flow on Reynolds number and fluid vortex frequency as two main parameters in creation of Lock-in phenomenon is studied. In addition to effect of different fluid velocities, response of the micro-beam to different input voltages in the presence of fluid flow is investigated and it is shown that for a given flowing fluid, applied voltage can be used to control the lock-in regime.