An Experimental and Theoretical Investigation of Nonlinear Vibrations of Piezoelectrically-Driven Microcantilevers

Abstract

The nonlinear vibrations of a piezoelectrically-driven microcantilever beam are experimentally and theoretically investigated. A part of the microcantilever beam surface is covered by a piezoelectric layer, which acts as an actuator. Practically, the first resonance of the beam is of interest, and hence, the microcantilever beam is modeled to obtain the natural frequency theoretically. The bending vibrations of the beam are studied considering the inextensibility condition and the coupling between electrical and mechanical properties in piezoelectric materials. The nonlinear term appears in the form of quadratic due to presence of piezoelectric layer, and cubic form due to geometry of the beam (mainly due to the beam's inextensibility). Galerkin approximation is utilized to discretize the equations of motion. The obtained equation is simulated to find the natural frequency of the system. In addition, method of multiple scales is applied to the equations of motion to arrive at the closed-form solution for natural frequency of the system. The experimental results verify the theoretical findings very closely. It is, therefore, concluded that the nonlinear approach could provide better dynamic representation of the microcantilever than previous linear models.