Experimental Enhanced Nonlinear Dynamics and Identification of Attractor Morphing Modes for Damage Detection

Abstract

This paper demonstrates two novel methods for identifying small parametric variations in an experimental system based on the analysis of sensitivity vector fields (SVFs) and probability density functions (PDFs). The experimental system includes a smart sensing beam excited by a nonlinear feedback excitation through two lead zirconate titanate patches symmetrically bonded on both sides at the root of the beam. The nonlinear feedback excitation requires the measurement of the dynamics (e.g., velocity of one point at the tip of the beam) and a nonlinear feedback loop, and is designed such that the beam vibrates in a chaotic regime. Changes in the state space attractor of the dynamics due to small parametric variations can be captured by SVFs, which, in turn, are collected by applying point cloud averaging to points distributed in the attractors for nominal and changed parameters. Also, the PDFs characterize statistically the distribution of points in the attractors. The differences between the PDFs of the attractors for different changed parameters and the base line attractor can provide different attractor morphing modes for identifying variations in distinct parameters. Experimental results based on the proposed approaches show that very small amounts of added mass at different locations along the beam can be accurately identified.2