The Passage of Weakly Coupled Nonlinear Oscillators through Internal Resonance

1977 ◽  
Vol 57 (1) ◽  
pp. 77-92 ◽  
Author(s):  
L. A. Rubenfeld
Keyword(s):  
Internal Resonance ◽  
Nonlinear Oscillators ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators

Motion of two weakly coupled nonlinear oscillators

1965 ◽  
Vol 18 (4) ◽  
pp. 293-303 ◽  
Author(s):  
Thomas G. Proctor ◽  
Raimond A. Struble
Keyword(s):  
Nonlinear Oscillators ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators

Chaos and nonisochronism in weakly coupled nonlinear oscillators

1991 ◽  
Vol 44 (6) ◽  
pp. 3452-3456 ◽  
Author(s):  
M. Poliashenko ◽  
S. R. McKay ◽  
C. W. Smith
Keyword(s):  
Nonlinear Oscillators ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators

Experimental observations of nonlinear vibration localization in a cyclic chain of weakly coupled nonlinear oscillators

2021 ◽  
Vol 497 ◽  
pp. 115952
Author(s):  
B. Niedergesäß ◽  
A. Papangelo ◽  
A. Grolet ◽  
A. Vizzaccaro ◽  
F. Fontanela ◽  
...  
Keyword(s):  
Nonlinear Vibration ◽  
Nonlinear Oscillators ◽  
Vibration Localization ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators

Frequency Clustering in a Chain of Weakly Coupled Oscillators

1997 ◽  
Vol 52 (8-9) ◽  
pp. 578-580 ◽  
Author(s):  
Thomas Kirner ◽  
Otto E. Rössler
Keyword(s):  
Numerical Simulation ◽  
Small Intestine ◽  
Coupled Oscillators ◽  
Nonlinear Oscillators ◽  
Conduction System ◽  
Linear Parameter ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators ◽  
A Chain ◽  
Frequency Gradient

Abstract A numerical simulation of a chain of diffusively coupled nonlinear oscillators with a linear parameter gradient exhibits clusters of frequencies. The intention was to investigate the frequency-gradient in the stimulus conduction system of the heart. The phenomenon generalizes earlier findings on “frequency plateaus” described in the 1960's by Nicholas Diamant as a model of small-intestine transport. This “waxing and waining” phenomenon is a version of chaos. Thus, subtle chaos in the heart and waxing and waining type chaos in the intestine may be related.

scholarly journals Simultaneous normal form transformation and model-order reduction for systems of coupled nonlinear oscillators

2019 ◽  
Vol 475 (2228) ◽  
pp. 20190042 ◽  
Author(s):  
X. Liu ◽  
D. J. Wagg
Keyword(s):  
Normal Form ◽  
Internal Resonance ◽  
Low Frequency ◽  
Order Reduction ◽  
Nonlinear Oscillators ◽  
Transformation Process ◽  
Accurate Solution ◽  
Coupled Nonlinear Oscillators ◽  
Form Transformation ◽  
Normal Form Transformation

In this paper, we describe a direct normal form decomposition for systems of coupled nonlinear oscillators. We demonstrate how the order of the system can be reduced during this type of normal form transformation process. Two specific examples are considered to demonstrate particular challenges that can occur in this type of analysis. The first is a 2 d.f. system with both quadratic and cubic nonlinearities, where there is no internal resonance, but the nonlinear terms are not necessarily ε 1 -order small. To obtain an accurate solution, the direct normal form expansion is extended to ε 2 -order to capture the nonlinear dynamic behaviour, while simultaneously reducing the order of the system from 2 to 1 d.f. The second example is a thin plate with nonlinearities that are ε 1 -order small, but with an internal resonance in the set of ordinary differential equations used to model the low-frequency vibration response of the system. In this case, we show how a direct normal form transformation can be applied to further reduce the order of the system while simultaneously obtaining the normal form, which is used as a model for the internal resonance. The results are verified by comparison with numerically computed results using a continuation software.

scholarly journals Nonlinear vibration localisation in a symmetric system of two coupled beams

2020 ◽  
Author(s):  
Filipe Fontanela ◽  
Alessandra Vizzaccaro ◽  
Jeanne Auvray ◽  
Björn Niedergesäß ◽  
Aurélien Grolet ◽  
...  
Keyword(s):  
Experimental Investigation ◽  
Nonlinear Vibration ◽  
Piecewise Linear ◽  
Nonlinear Oscillators ◽  
Symmetric System ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators ◽  
Coupled Beams ◽  
Two Degree Of Freedom ◽  
Piecewise Linear Stiffness

Abstract We report nonlinear vibration localisation in a system of two symmetric weakly coupled nonlinear oscillators. A two degree-of-freedom model with piecewise linear stiffness shows bifurcations to localised solutions. An experimental investigation employing two weakly coupled beams touching against stoppers for large vibration amplitudes confirms the nonlinear localisation.

Nonlinear Dynamics of Coupled Nonlinear Oscillators: Using of Complex Variables

1999 ◽  
Author(s):  
L. I. Manevitch
Keyword(s):  
Nonlinear Dynamics ◽  
Strong Coupling ◽  
Degrees Of Freedom ◽  
Normal Modes ◽  
Nonlinear Oscillators ◽  
Complex Variables ◽  
Dynamic Equations ◽  
Asymptotic Approach ◽  
Weakly Coupled ◽  
Coupled Nonlinear Oscillators

Abstract We present an asymptotic approach to the analysis of coupled nonlinear oscillators with asymmetric nonlinearity based on the complex representation of the dynamic equations The ideas of the approach are previously given on the example of the system with two degrees of freedom. The special attention is paid to the study of localized normal modes in the chain of weakly coupled nonlinear oscillators. We discuss also certain peculiarities of the localization of excitations in the case of strong coupling between oscillators.

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