Nonlinear Periodic Systems with Mode Localization and Motion Confinement Characteristics

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The principal scope of the proposed work is to show that weakly coupled, flexible, cyclic assemblies with geometric nonlinearities due to finite-amplitude motions, possess localized nonlinear modes, i.e., free oscillations during which the motion is mainly confined to only one of their subsystems. This will be achieved by using a multiple-scales averaging methodology and studying the corresponding amplitude and phase modulation equations. The effects of internal resonances between flexible modes on the mode localization will be analytically investigated and the force responses of the system due to external harmonic loads will be considered. It will be shown that weakly coupled cyclic assemblies possess fundamental, subharmonic and superharmonic localized resonances, during which only a limited number of their subsystems resonate. Motion confinement of externally generated disturbances due to nonlinear mode localization will then be investigated by numerical computations, involving finite element and Gallerkin methodologies. The principal aim of this study is to show that the inherent dynamics of certain weakly coupled, nonlinear cyclic systems, lead to motion confinement of externally induced disturbances. The controllability of such systems is then greatly improved, since in designing for passive or active vibration isolation, one needs only consider the dynamics of a limited number of their substructure instead of considering the response of the whole cyclic assembly.*** //