Experimental system identification of the dynamics of a vibro-impact beam with a view towards structural health monitoring and damage detection

• Nonlinear system identification of experimental vibro-impact beam responses.
• EMD analysis to separate nonsmooth effects from the elastodynamic responses.
• Construction of spatiotemporal variations of nonlinear modal interactions.
• MAC/COMAC for structural health monitoring (SHM)/damage detection (DD).

We perform nonlinear system identification (NSI) on the acceleration signals that were experimentally measured at ten, almost evenly spaced positions along a cantilever beam undergoing vibro-impacts between two rigid stops with clearances. Our goal is to characterize the nonlinear dynamics due to vibro-impacts with a view toward structural health monitoring (SHM) and damage detection (DD). The NSI methodology is based on the correspondence between analytical and empirical slow-flow dynamics, with the first step requiring empirical mode decomposition (EMD) analysis of the measured time series leading to sets of intrinsic modal oscillators (IMOs) governing the vibro-impact dynamics at different time scales. By comparing the spatiotemporal variations of the nonlinear modal interactions (and hence the IMOs), we examine how vibro-impacts influence the low- and high-frequency modes in global and local senses. In applications of the NSI results to SHM/DD, we calculate typical measures such as the modal assurance criterion (MAC) and the coordinate modal assurance criterion (COMAC) by extracting information about the mode shape functions from the spatiotemporal IMO solutions. Whereas the MAC provides a global aspect of damage occurrence (i.e., which modes are more affected by induced defects), the COMAC can narrow down the damage locations (i.e., where in the structure defects exist that yield low correlation values in specific modes).