Global dynamics of composite panels with free-layer damping treatment in subsonic flow

Abstract

Global dynamics of forcedly excited composite panels with free layer damping treatment in subsonic flow near the first-order critical velocity is investigated. Hamilton’s principle is implemented to derive the PDE of such fluid-structure interaction systems. Then the governing equation is transformed into a discretized nonlinear gyroscopic system via assumed modes and Galerkin’s method. The canonical transformations and normal form theory are applied to reduce the equations of motion to near-integrable Hamiltonian standard forms considering zero to one internal resonance. The Energy-Phase method is employed to demonstrate the existence of chaotic dynamics by identifying the existence of multi-pulse jumping orbits in the perturbed phase space. In both the Hamiltonian and the dissipative perturbation case, the homoclinic trees which describe the repeated bifurcations of multi-pulse solutions are demonstrated. In the case of dissipative perturbation, the existence of generalized Šilnikov’s type of orbits which are homoclinic to fixed points on the slow manifold are examined and the parameter region for which the dynamical system may exhibit chaotic motions in the sense of Smale horseshoes are obtained analytically. The present research illustrates that the existence of multi-pulse homoclinic orbits can provide a mechanism for how energy flow from the high-frequency mode to the low-frequency mode. The global results are finally interpreted in terms of the physical traveling wave motion of such gyroscopic continua.