Nonlinear system identification of the dynamics of a vibro-impact beam

We study the dynamics of a cantilever beam with two rigid stops of certain clearances by performing nonlinear system identification (NSI) based on the correspondence between analytical and empirical slow-flow dynamics. First, we perform empirical mode decomposition (EMD) on the acceleration responses measured at ten, almost evenly-spaced, spanwise positions along the beam leading to sets of intrinsic modal oscillators governing the vibroimpact dynamics at different time scales. In particular, the EMD analysis can separate any nonsmooth effects caused by vibro-impacts of the beam and the rigid stops from the smooth (elastodynamic) response, so that nonlinear modal interactions caused by vibro-impacts can be explored only with the remaining smooth components. Then, we establish nonlinear interaction models (NIMs) for the respective intrinsic modal oscillators, where the NIMs invoke slowly-varying forcing amplitudes that can be computed from empirical slow-flows. By comparing the spatio-temporal variations of the nonlinear modal interactions for the vibro-impact beam and those of the underlying linear model (i.e., the beam with no rigid constraints), we demonstrate that vibro-impacts significantly influence the lower frequency modes introducing spatial modal distortions, whereas the higher frequency modes tend to retain their linear dynamics in between impacts.