Combination resonances in the response of the duffing oscillator to a three-frequency excitation

1998 ◽  
Vol 131 (3-4) ◽  
pp. 235-245 ◽  
Author(s):  
S. Yang ◽  
A. H. Nayfeh ◽  
D. T. Mook
Keyword(s):  
Duffing Oscillator ◽  
Frequency Excitation

scholarly journals Control of Bistability in a Delayed Duffing Oscillator

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
Mustapha Hamdi ◽  
Mohamed Belhaq
Keyword(s):  
Hopf Bifurcation ◽  
Multiple Scales ◽  
Duffing Oscillator ◽  
Stable Limit Cycle ◽  
Slow Flow ◽  
Stable Limit ◽  
Nontrivial Solutions ◽  
Slow Dynamic ◽  
High Frequency Excitation ◽  
Frequency Excitation

The effect of a high-frequency excitation on nontrivial solutions and bistability in a delayed Duffing oscillator with a delayed displacement feedback is investigated in this paper. We use the technique of direct partition of motion and the multiple scales method to obtain the slow dynamic of the system and its slow flow. The analysis of the slow flow provides approximations of the Hopf and secondary Hopf bifurcation curves. As a result, this study shows that increasing the delay gain, the system undergoes a secondary Hopf bifurcation. Further, it is indicated that as the frequency of the excitation is increased, the Hopf and secondary Hopf bifurcation curves overlap giving birth in the parameter space to small regions of bistability where a stable trivial steady state and a stable limit cycle coexist. Numerical simulations are carried out to validate the analytical finding.

Strong chaotification and robust chaos in the Duffing oscillator induced by two-frequency excitation

2021 ◽  
Vol 103 (2) ◽  
pp. 1955-1967
Author(s):  
André Gusso ◽  
Sebastian Ujevic ◽  
Ricardo L. Viana
Keyword(s):  
Duffing Oscillator ◽  
Frequency Excitation

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

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.

scholarly journals Chaos in the quantum Duffing oscillator in the semiclassical regime under parametrized dissipation

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Andrew D. Maris ◽  
Bibek Pokharel ◽  
Sharan Ganjam Seshachallam ◽  
Moses Z. R. Misplon ◽  
Arjendu K. Pattanayak
Keyword(s):  
Duffing Oscillator ◽  
Semiclassical Regime
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