NDLI: Energy exchange and localization in the planar motion of a weightless beam carrying two discrete masses

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Energy exchange and localization in the planar motion of a weightless beam carrying two discrete masses

Content Provider	Springer Nature Link
Author	Silina, Kseniya G. Kikot, Irina P. Manevitch, Leonid I.
Copyright Year	2015
Abstract	We present analytical and numerical studies of nonstationary resonance processes in a system with four degrees of freedom. The system under consideration can be considered as one of the simplest geometrically nonlinear discrete models of an elastic beam supported by nonlinear elastic grounding support. Two symmetrically distributed discrete masses reflect the inertial properties of the beam, two angular springs simulate its bending stiffness. The longitudinal springs, as is usual in systems of oscillators, reflect the tensile stiffness and two transversal springs simulate the reaction of grounding support. Dealing with low-energy dynamics, we singled out the equations of transversal motion corresponding to the approximation of two coupled oscillators with nonlocal nonlinearity in elastic forces. We have analyzed this model using the concept of limiting phase trajectories (LPT). LPT’s concept was recently developed to study the nonstationary resonance dynamics. An analytical description of intensive interparticle energy exchange was obtained in terms of nonsmooth functions, which is consistent with numerical results. We have identified two dynamic transitions the first of which corresponds to the instability of out-of-phase normal mode and the second one is a transition from the intense energy exchange to the energy localization on the initially excited oscillator. Special attention was paid to the influence of bending stiffness on the conditions that ensure the implementation of each of the dynamic transitions.
Starting Page	109
Ending Page	122
Page Count	14
File Format	PDF
ISSN	15603547
Journal	Regular and Chaotic Dynamics
Volume Number	20
Issue Number	2
e-ISSN	14684845
Language	English
Publisher	Pleiades Publishing
Publisher Date	2015-05-07
Publisher Place	Moscow
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	energy exchange energy localization beam elastic support nonlinear normal modes limiting phase trajectories Dynamical Systems and Ergodic Theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Statistical and Nonlinear Physics Mathematical Physics Mechanical Engineering Modeling and Simulation

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