Multi-scale energy exchanges between a nonlinear oscillator of Bouc-Wen type and another coupled nonlinear system

2013 ◽  
Vol 222 (7) ◽  
pp. 1617-1636 ◽  
Author(s):  
C.-H. Lamarque ◽  
A. Ture Savadkoohi ◽  
M. Naudan
2015 ◽  
Vol 83 (1-2) ◽  
pp. 109-135 ◽  
Author(s):  
Mathieu Weiss ◽  
Mahmoud Chenia ◽  
Alireza Ture Savadkoohi ◽  
Claude-Henri Lamarque ◽  
Bastien Vaurigaud ◽  
...  

1996 ◽  
Vol 06 (12b) ◽  
pp. 2557-2570 ◽  
Author(s):  
H. FRANCO

A forced nonlinear oscillator can exhibit complex transient spectra even in the absence of chaotic phenomena. Series of evenly spaced lines appear in spectrograms of the numerically computed oscillations. They can be explained by means of a simple model describing the dynamics of the energy exchange between the external oscillating force and the nonlinear system. The resulting amplitude and phase modulations are shown to produce the spectral line structures. Frequencies incommensurable with other present frequencies can be generated by the nonlinear system.


Author(s):  
Jérôme Weiss ◽  
Véronique Dansereau

Mechanics plays a key role in the evolution of the sea ice cover through its control on drift, on momentum and thermal energy exchanges between the polar oceans and the atmosphere along cracks and faults, and on ice thickness distribution through opening and ridging processes. At the local scale, a significant variability of the mechanical strength is associated with the microstructural heterogeneity of saline ice, however characterized by a small correlation length, below the ice thickness scale. Conversely, the sea ice mechanical fields (velocity, strain and stress) are characterized by long-ranged (more than 1000 km) and long-lasting (approx. few months) correlations. The associated space and time scaling laws are the signature of the brittle character of sea ice mechanics, with deformation resulting from a multi-scale accumulation of episodic fracturing and faulting events. To translate the short-range-correlated disorder on strength into long-range-correlated mechanical fields, several key ingredients are identified: long-ranged elastic interactions, slow driving conditions, a slow viscous-like relaxation of elastic stresses and a restoring/healing mechanism. These ingredients constrained the development of a new continuum mechanics modelling framework for the sea ice cover, called Maxwell–elasto-brittle. Idealized simulations without advection demonstrate that this rheological framework reproduces the main characteristics of sea ice mechanics, including anisotropy, spatial localization and intermittency, as well as the associated scaling laws. This article is part of the themed issue ‘Microdynamics of ice’.


Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 535 ◽  
Author(s):  
Thoai Phu Vo ◽  
Yeganeh Shaverdi ◽  
Abdul Jalil M. Khalaf ◽  
Fawaz E. Alsaadi ◽  
Tasawar Hayat ◽  
...  

In this paper, inspired by a newly proposed two-dimensional nonlinear oscillator with an infinite number of coexisting attractors, a modified nonlinear oscillator is proposed. The original system has an exciting feature of having layer–layer coexisting attractors. One of these attractors is self-excited while the rest are hidden. By forcing this system with its twin, a new four-dimensional nonlinear system is obtained which has an infinite number of coexisting torus attractors, strange attractors, and limit cycle attractors. The entropy, energy, and homogeneity of attractors’ images and their basin of attractions are calculated and reported, which showed an increase in the complexity of attractors when changing the bifurcation parameters.


2006 ◽  
Vol 2006 ◽  
pp. 1-19 ◽  
Author(s):  
J. Warminski ◽  
K. Kecik

Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It has been found that the motion of the oscillator, forced by an external harmonic force, has been dynamically eliminated by the pendulum oscillations. Influence of a nonlinear spring on the vibration absorption near the main parametric resonance region has been carried out analytically, whereas the transition from regular to chaotic vibrations has been presented by using numerical methods. A transmission force on the foundation for regular and chaotic vibrations is presented as well.


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