Nonlinear Vibrations of a Piezoelectrically-Driven Microcantilever for Biologically-Induced Surface Stress Sensing

Abstract

In this paper, nonlinear vibrations of a piezoelectrically-driven microcantilever beam in presence of a biological monolayer are investigated and the corresponding equations of motion are derived and simulated. A part of the microcantilever beam surface is covered by a piezoelectric layer, which acts as an actuator. Inextensibility condition and the coupling between electrical and mechanical properties in piezoelectric materials are considered in the bending vibrations of the beam. The adsorbed biological layer is considered to be a monolayer and its adsorption induced surface stress is formulated from the molecular viewpoint. The nonlinear terms in the governing equations of motion of the beam appear in the form of quadratic due to presence of piezoelectric layer, and cubic due to geometry of the beam and the adsorbed biological layer. Through extensive numerical simulations, it is demonstrated that the nonlinear effect of piezoelectric layer is significant in the microcantilever resonance sensing range. It is also shown that the effect of intermolecular attraction/repulsion on the surface stress is less dominant than other sources of surface stress (e.g., the electrostatic forces). Finally, it is observed that piezoelectrically-actuated microcantilever provides the ability of indirect measurement of vibrations and frequency response characteristics, instead of using bulky laser sensor.