Limiting Phase Trajectories as an Alternative to Nonlinear Normal Modes
نویسندگان
چکیده
منابع مشابه
Resonant energy exchange in nonlinear oscillatory chains and Limiting Phase Trajectories : from small to large systems
We present an adequate analytical approach to the description of nonlinear vibration with strong energy exchange between weakly coupled oscillators and oscillatory chains. The fundamental notion of the limiting phase trajectory (LPT) corresponding to complete energy exchange is introduced. In certain sense this is an alternative to the nonlinear normal mode (NNM) characterized by complete energ...
متن کاملNonlinear Normal Modes, Part I: An Attempt To Demystify Them
The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companions, Parts II and III. Because there is virtually no application of the NNMs to large-scale engineering structures, these papers are an attempt to highlight several aspects that might drive their development in the future. Specifically, we support that (i) numerical methods for the continuation of peri...
متن کاملLimiting phase trajectories and the origin of energy localization in nonlinear oscillatory chains.
We demonstrate that the modulation instability of the zone-boundary mode in a finite (periodic) Fermi-Pasta-Ulam chain is the necessary but not sufficient condition for the efficient energy transfer by localized excitations. This transfer results from the exclusion of complete energy exchange between spatially different parts of the chain, and the excitation level corresponding to that turns ou...
متن کاملRelative Nonlinear Normal Modes of Hamiltonian Systems
We generalize theWeinstein-Moser theorem on the existence of nonlinear normal modes (i.e., periodic orbits) near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. More specifically we significantly improve a result proved earlier jointly with Tokieda: we remove a techni...
متن کاملRelative normal modes for nonlinear Hamiltonian systems
An estimate on the number of distinct relative periodic orbits around a stable relative equilibrium in a Hamiltonian system with continuous symmetry is given. This result constitutes a generalization to the Hamiltonian symmetric framework of a classical result by Weinstein and Moser on the existence of periodic orbits in the energy levels surrounding a stable equilibrium.The estimate obtained i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Procedia IUTAM
سال: 2016
ISSN: 2210-9838
DOI: 10.1016/j.piutam.2016.03.019