Abstract
Periodic structures with cyclic symmetry are often used as idealized models of physical systems including bladed-disk assemblies, large space antennas, circular saws and disks, and flexible magnetic storage media. The present work considers a simplified model of such structures and investigates the nonlinear vibratory response to periodic excitations. The model consists of n identical particles, arranged in a circular ring, interconnected by extensional springs with linear and nonlinear stiffness characteristics, and hinged to the ground individually by nonlinear torsional springs. When the linear couping stiffness is O(ε), the cyclic system consists of n weakly coupled identical nonlinear oscillators so that all the oscillators are in internal resonance. The dynamic response of this system to resonant periodic excitation is studied using the method of averaging. The amplitude equations consist of a 2n system of first order ordinary differential equations that depend on the forcing amplitude and frequency, the modal damping, and the nature of the excitation. These equations are analyzed using local bifurcation theory, and the effects of coupling strength to nonlinearity parameter on the steady-state responses are determined. It is found that when only one particle is excited, the response for very weak coupling essentially remains localized. For larger coupling strength, both localized and extended responses are found over different excitation frequency intervals.
