The effect of a piezoelectric layer on the mechanical behavior of an electrostatic actuatedmicrobeam

Abstract

In this paper, the deflection and natural frequency of a microbeam under combinedelectrostatic and piezoelectric actuations is obtained for the first time. The microbeam hasbeen assumed as a composite Euler–Bernoulli beam with a piezoelectric layerdeposited on it. The nonlinear equation of motion has been derived using theHamilton principle, and solved using the Galerkin method. It is assumed that theneutral axis of bending is stretched when the beam is deflected. The axial load orpre-stress has been considered in derivations of the motion equations, and theboundary conditions in transverse vibration are assumed as clamped–clamped. Ithas been shown that the pull-in voltage, natural frequency and deflection of thesystem depend on the value of electrostatic actuation and the location, thicknessand applied voltage of the piezoelectric layer. Thus the deflection and naturalfrequency of an electrostatic actuated microbeam may be tuned to a suitablevalue by altering the applied voltage to the piezoelectric layer, which is moreconvenient than altering the axial load, as used in previous methods. Also, this showsthat a new sensor–actuator system may be constructed which is actuated byapplying the voltage to the piezoelectric layer, and this actuation is sensed bythe value of the output electric current induced from movement of the polarizedmicrobeam.