Duffing oscillation and jump resonance: Spectral hysteresis and input-dependent resonance shift

Abstract

The purpose of this paper is to present experimental results for jump resonance observed in a vibrating cantilever beam of a macro-scale atomic force microscope (AFM), and to connect these results with the well-known Duffing nonlinear oscillator dynamics. The paper gives a review of the theoretical analyses of such behaviors, as well as detailed experimental results for nonlinear frequency-domain jump resonance in the vibrating AFM probe. The experimental results clearly show the model-predicted input-dependent resonant frequency shift. A real-time simulation model of the experimental system is also presented as a useful tool to understand the nonlinear dynamic structure, as an aid in identifying the Duffing equation parameters, and allow simulation studies of ideas such as controlling the nonlinear system behavior. We also present a feedback linearization algorithm to compensate for the cubic stiffness internal to the Duffing nonlinear oscillator. The simple experimental system described herein can be easily and inexpensively constructed to allow students and researchers to conduct their own experiments with such nonlinear dynamics.