Application of piezoelectric actuation to regularize the chaotic response of an electrostatically actuated micro-beam

Abstract

The impetus of this study is to investigate the nonlinear chaotic dynamics of a clamped–clamped micro-beam exposed to simultaneous electrostatic and piezoelectric actuation. The micro-beam is sandwiched with piezoelectric layers throughout its length. The combined DC and AC electrostatic actuation is imposed on the micro-beam through two upper and lower electrodes. The piezoelectric layers are actuated via a DC electric voltage applied in the direction of the height of the piezoelectric layers, which produces an axial force proportional to the applied DC voltage. The governing differential equation of the motion is derived using Hamiltonian principle and discretized to a nonlinear Duffing type ODE using Galerkin method. The governing ODE is numerically integrated to get the response of the system in terms of the governing parameters. The results show that the response of the system is greatly affected by the amounts of DC and AC electrostatic voltages applied to the upper and lower electrodes. The results show that the response of the system can be highly nonlinear and in some regions chaotic. Evaluating the K–S entropy of the system, based on several initial conditions given to the system, the chaotic response is distinguished from the periodic or quasiperiodic ones. The main objective is to passively control the chaotic response by applying an appropriate DC voltage to the piezoelectric layers.