Nonlinear Vibration Localization in Cyclic Structures
Many mechanical structures in engineering and technology, like rotors, turbines, compressors etc, are cyclically assembled in the form of nearly identical components. The operational loads are often unsteady and lead to vibrations that determine or limit the function or lifetime of the systems. Often vibrations result that are not homomogeneously spread out over the whole system, but are confined to certain spatial zones only: localized vibrations. In the context of linear system models, slight inhomogeneities or perturbations of the symmetry explain localization very well. Rather recently, however, it has become more obvious that such cyclic systems also bear marked nonlinear properties. Which bring along novel nonlinear vibration phenomena. One class of such nonlinear vibrations are nonlinearly localized vibrations, which is the topic of the present project. From nonlinear dynamics in general it is well known that there are certain mechanisms that may lead to nonlinearly localized dynamics. While for many fields in science such nonlinear localization has been studied for a long time, and its relevance is widely acknowledged, for nonlinear mechanical vibrations the understanding is still comparatively limited. In nonlinear vibrations, the amplitude-dependent frequency shifts of single nonlinear oscillators may lead to a reduced coupling to neighbouring oscillators, which under certain conditions may result in full spatial localization of the vibration. In the present project the starting point will be the so-called discrete breathers. Conceptual, numerical, and experimental studies, based on a model system, are to be conducted to characterize and quantify the phenomena related with nonlinear vibration localization. We will aim at answering, under what system and loading conditions nonlinear vibration localization appears, and how robust or stable it is. Further topics of the study are the emergence of extended domains of localized vibration, the transition regeion between zones of strong and weak or no vibration, and the interplay between linear and nonlinear localization mechanisms.