Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators
Joint Authors
Kovaleva, A. S.
Manevitch, E. L.
Manevitch, L. I.
Source
Mathematical Problems in Engineering
Issue
Vol. 2010, Issue 2010 (31 Dec. 2010), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2010-03-01
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
We study a problem of energy exchange in a system of two coupled oscillators subject to 1 : 1 resonance.
Our results exploit the concept of limiting phase trajectories (LPTs).
The LPT, associated with full energy transfer, is, in certain sense, an alternative to nonlinear normal modes characterized by conservation of energy.
We consider two benchmark examples.
As a first example, we construct an LPT and examine the convergence to stationary oscillations for a Duffing oscillator subjected to resonance harmonic excitation.
As a second example, we treat resonance oscillations in a system of two nonlinearly coupled oscillators.
We demonstrate the reduction of the equations of motion to an equation of a single oscillator.
It is shown that the most intense energy exchange and beating arise when motion of the equivalent oscillator is close to an LPT.
Damped beating and the convergence to rest in a system with dissipation are demonstrated.
American Psychological Association (APA)
Manevitch, L. I.& Kovaleva, A. S.& Manevitch, E. L.. 2010. Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators. Mathematical Problems in Engineering،Vol. 2010, no. 2010, pp.1-24.
https://search.emarefa.net/detail/BIM-496605
Modern Language Association (MLA)
Manevitch, L. I.…[et al.]. Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators. Mathematical Problems in Engineering No. 2010 (2010), pp.1-24.
https://search.emarefa.net/detail/BIM-496605
American Medical Association (AMA)
Manevitch, L. I.& Kovaleva, A. S.& Manevitch, E. L.. Limiting Phase Trajectories and Resonance Energy Transfer in a System of Two Coupled Oscillators. Mathematical Problems in Engineering. 2010. Vol. 2010, no. 2010, pp.1-24.
https://search.emarefa.net/detail/BIM-496605
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-496605