Resonant Layers in Nonlinear Dynamics

1998 ◽  
Vol 65 (3) ◽  
pp. 727-736 ◽  
Author(s):  
R. P. S. Han ◽  
A. C. J. Luo
Keyword(s):  
Nonlinear Dynamics ◽  
Renormalization Group ◽  
Numerical Simulations ◽  
Duffing Oscillator ◽  
Energy Approach ◽  
New Method ◽  
Mapping Technique ◽  
Standard Mapping ◽  
Left And Right ◽  
Group Technique

A new method based on an incremental energy approach and the standard mapping technique is proposed for the study of resonant layers in nonlinear dynamics. To demonstrate the procedure, the method is applied to four types of Duffing oscillators. The appearance, disappearance and accumulated disappearance strengths of the resonant layers for each type of oscillator are derived. A quantitative check of the appearance strength is performed by computing its value using three independent methods: Chirikov overlap criterion, renormalization group technique, and numerical simulations. It is also observed that for the case of the twin-well Duffing oscillator, its perturbed left and right wells are asymmetric.

Investigations of Stochastic Layers in Nonlinear Dynamics

1999 ◽  
Vol 122 (1) ◽  
pp. 36-41 ◽  
Author(s):  
Albert C. J. Luo ◽  
Ray P. S. Han
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Investigation ◽  
Duffing Oscillator ◽  
Minimum Energy ◽  
Energy Approach ◽  
Energy Spectra ◽  
Poincaré Mapping ◽  
Periodically Driven ◽  
Poincare Mapping ◽  
Stochastic Layer

The onset of a new resonance in the stochastic layer is predicted numerically through the maximum and minimum energy spectra when the energy jump in the spectra occurs. The incremental energy approach among all the established, analytic approaches gives the best prediction of the onset of resonance in the stochastic layer compared to numerical investigation. The stochastic layers in the periodically-driven pendulum are discussed as another example. Illustrations of stochastic layers in the twin-well Duffing oscillator and the periodically-driven pendulum are given through the Poincare´ mapping sections. [S0739-3717(00)00701-7]

Resonant Bands of a Mathieu-Duffing Oscillator With a Twin-Well Potential

2002 ◽  
Author(s):  
Albert C. J. Luo
Keyword(s):  
Parametric Excitation ◽  
Duffing Oscillator ◽  
Resonance Interaction ◽  
Energy Approach ◽  
Potential Wells ◽  
Spectrum Method ◽  
Numerical Predictions ◽  
Left And Right ◽  
Energy Increment

The (M:1)-resonant bands in the left and right potential wells are skew-symmetric, and the (2M:1)-resonant bands of the large orbit motion are symmetric. The analytical conditions for the onset and destruction of a resonant band are developed through the incremental energy approach. The numerical predictions of such the onset and destruction are also completed by the energy increment spectrum method. The sub-resonance interaction occurs for strong excitations, which needs to be further investigated. These results are applicable to the small orbit and large orbit motions of post-buckled structure under a parametric excitation.

Suppressing Chaos in a Nonideal Double-Well Oscillator Using an Based Electromechanical Damped Device

2014 ◽  
Vol 706 ◽  
pp. 25-34 ◽  
Author(s):  
G. Füsun Alişverişçi ◽  
Hüseyin Bayiroğlu ◽  
José Manoel Balthazar ◽  
Jorge Luiz Palacios Felix
Keyword(s):  
Numerical Simulations ◽  
Chaotic Dynamics ◽  
Duffing Oscillator ◽  
Vibration Energy ◽  
Vibration Absorber ◽  
Electrical System ◽  
Chaotic Vibration ◽  
System A ◽  
Ideal System ◽  
Double Well Potential

In this paper, we analyzed chaotic dynamics of an electromechanical damped Duffing oscillator coupled to a rotor. The electromechanical damped device or electromechanical vibration absorber consists of an electrical system coupled magnetically to a mechanical structure (represented by the Duffing oscillator), and that works by transferring the vibration energy of the mechanical system to the electrical system. A Duffing oscillator with double-well potential is considered. Numerical simulations results are presented to demonstrate the effectiveness of the electromechanical vibration absorber. Lyapunov exponents are numerically calculated to prove the occurrence of a chaotic vibration in the non-ideal system and the suppressing of chaotic vibration in the system using the electromechanical damped device.

Dynamics of a Supported Cylinder in Axial Flow

2011 ◽  
Vol 99-100 ◽  
pp. 1059-1062
Author(s):  
Ji Duo Jin ◽  
Ning Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Analysis ◽  
Numerical Simulations ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Friction Drag ◽  
Flutter Instability ◽  
Nonlinear Force

The nonlinear dynamics are studied for a supported cylinder subjected to axial flow. A nonlinear model is presented for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the structural nonlinear force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain the flutter instability found in the experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. The effect of the friction drag coefficients on the behavior of the system is investigated.

scholarly journals Pinning-Like Adaptive Consensus for Networked Mobile Agents with Heterogeneous Nonlinear Dynamics

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Chengjie Xu ◽  
Yanwei Wang ◽  
Hong Zhang ◽  
Xiaoqi Zhou
Keyword(s):  
Nonlinear Dynamics ◽  
Adaptive Control ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Mobile Agents ◽  
Pinning Control ◽  
Adaptive Strategy ◽  
Global Information ◽  
First Order ◽  
Coupling Strengths

This paper investigates the adaptive consensus for networked mobile agents with heterogeneous nonlinear dynamics. Using tools from matrix, graph, and Lyapunov stability theories, sufficient consensus conditions are obtained under adaptive control protocols for both first-order and second-order cases. We design an adaptive strategy on the coupling strengths, which can guarantee that the consensus conditions do not require any global information except a connection assumption. The obtained results are also extended to networked mobile agents with identical nonlinear dynamics via adaptive pinning control. Finally, numerical simulations are presented to illustrate the theoretical findings.

scholarly journals Reversal Ventilation as a Method of Fire Hazard Mitigation in the Mines

Energies ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1755 ◽  
Author(s):  
Grzegorz Pach ◽  
Zenon Różański ◽  
Paweł Wrona ◽  
Adam Niewiadomski ◽  
Pavel Zapletal ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Fire Hazard ◽  
Full Range ◽  
Acceptable Level ◽  
New Method ◽  
Underground Mines ◽  
Operating Parameters ◽  
Smoke Control ◽  
Prevention Methods ◽  
Air Control

Reversal ventilation is one of prevention methods against fire hazard in underground mines, but it is not recommended for the mines where methane is present. The authors introduce the new method of reversal and by conducting numerical simulations they prove that it allows to keep methane at the acceptable level during miners escape. However, it requires connection between the subnetworks of the main ventilation fans. It was also shown, that by using the method some escape routes will be shortened. It is possible to apply this method in the mines where the fans and stoppings are fully controlled across the full range of their operating parameters. The findings are important for underground mines, as well as for surface facilities where air control or smoke control is managed by two or more fans.

Nonlinear dynamics of the elliptic instability

2010 ◽  
Vol 646 ◽  
pp. 471-480 ◽  
Author(s):  
NATHANAËL SCHAEFFER ◽  
STÉPHANE LE DIZÈS
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulations ◽  
Shear Layer ◽  
Rapid Growth ◽  
Vortex Core ◽  
Nonlinear Evolution ◽  
Core Size ◽  
Layer Formation ◽  
Vortex Loop ◽  
Weakly Nonlinear

In this paper, we analyse by numerical simulations the nonlinear dynamics of the elliptic instability in the configurations of a single strained vortex and a system of two counter-rotating vortices. We show that although a weakly nonlinear regime associated with a limit cycle is possible, the nonlinear evolution far from the instability threshold is, in general, much more catastrophic for the vortex. In both configurations, we put forward some evidence of a universal nonlinear transition involving shear layer formation and vortex loop ejection, leading to a strong alteration and attenuation of the vortex, and a rapid growth of the vortex core size.

Analytical Periodic Motions in a Periodically Forced, Damped Duffing Oscillator

2012 ◽  
Author(s):  
Albert C. J. Luo ◽  
Jianzhe Huang
Keyword(s):  
Numerical Simulations ◽  
Analytical Solutions ◽  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Approximate Solutions ◽  
Balance Method ◽  
Periodic Motions ◽  
Conditions Of Stability ◽  
Generalized Harmonic Balance Method

The analytical solutions of the period-1 motions for a hardening Duffing oscillator are presented through the generalized harmonic balance method. The conditions of stability and bifurcation of the approximate solutions in the oscillator are discussed. Numerical simulations for period-1 motions for the damped Duffing oscillator are carried out.

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