Localized Normal Modes in a Chain of Nonlinear Coupled Oscillators

2005 ◽  
pp. 169-189
Keyword(s):  
Coupled Oscillators ◽  
Normal Modes ◽  
Nonlinear Coupled Oscillators ◽  
A Chain

scholarly journals Standing wave instabilities in a chain of nonlinear coupled oscillators

2002 ◽  
Vol 162 (1-2) ◽  
pp. 53-94 ◽  
Author(s):  
Anna Maria Morgante ◽  
Magnus Johansson ◽  
Georgios Kopidakis ◽  
Serge Aubry
Keyword(s):  
Standing Wave ◽  
Coupled Oscillators ◽  
Nonlinear Coupled Oscillators ◽  
Wave Instabilities ◽  
A Chain

Bifurcation of Nonlinear Normal Modes by Means of Synge’s Stability

2011 ◽  
Author(s):  
Young S. Lee ◽  
Heng Chen
Keyword(s):  
Harmonic Balance ◽  
Coupled Oscillators ◽  
Normal Modes ◽  
Harmonic Balance Method ◽  
Orbital Stability ◽  
Nonlinear Normal Modes ◽  
Energy Transfers ◽  
Wide Range ◽  
Energy Domain ◽  
Nonlinear Normal

We study bifurcation of fundamental nonlinear normal modes (FNNMs) in 2-degree-of-freedom coupled oscillators by utilizing geometric mechanics approach based on Synges concept, which dictates orbital stability rather than Lyapunovs classical asymptotic stability. Use of harmonic balance method provides reasonably accurate approximation for NNMs over wide range of energy; and Floquet theory incorporated into Synges stability analysis predicts the respective bifurcation points as well as their types. Constructing NNMs in the frequency-energy domain, we seek applications to study of efficient targeted energy transfers.

On the Parameter Plane of Nonlinear Coupled Oscillators

1993 ◽  
Vol 48 (5-6) ◽  
pp. 655-662
Author(s):  
Wolfgang Metzler ◽  
Achim Brelle ◽  
Klaus-Dieter Schmidt ◽  
Gerrit Danker ◽  
Matthias Köppe ◽  
...  
Keyword(s):  
Coupled Oscillators ◽  
Nonlinear Oscillator ◽  
Mandelbrot Set ◽  
Parameter Plane ◽  
Two Dimensional ◽  
Routes To Chaos ◽  
Nonlinear Coupled Oscillators ◽  
Two Parameter

Abstract Two well-known bifurcation routes to chaos of two-dimensional coupled logistic maps are embedded in a two-parameter plane of a canonical nonlinear oscillator which contains a non-analytic analogon to the Mandelbrot set.

Random excitation of nonlinear coupled oscillators

1990 ◽  
Vol 1 (1) ◽  
pp. 91-116 ◽  
Author(s):  
R. A. Ibrahim ◽  
Y. J. Yoon ◽  
Michael G. Evans
Keyword(s):  
Coupled Oscillators ◽  
Random Excitation ◽  
Nonlinear Coupled Oscillators

Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.

1984 ◽  
Vol 15 (2) ◽  
pp. 215-237 ◽  
Author(s):  
George Bard Ermentrout ◽  
Nancy Kopell
Keyword(s):  
Coupled Oscillators ◽  
Weakly Coupled Oscillators ◽  
Weakly Coupled ◽  
A Chain
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