Ehrenfest Time at the Transition from Integrable Motion to Chaotic Motion

2021 ◽  
Vol 38 (3) ◽  
pp. 030502
Author(s):  
Chuan Zhao ◽  
Biao Wu
2002 ◽  
Author(s):  
Giulio Casati ◽  
Carlo Beenakker ◽  
Tomaz Prozen ◽  
Philippe Jacquod ◽  
Giuliano Benenti

1987 ◽  
Vol 43 (1-4) ◽  
pp. 361-369 ◽  
Author(s):  
M. Karch ◽  
R. Dvorak
Keyword(s):  

2003 ◽  
Vol 51 (4) ◽  
pp. 391-404 ◽  
Author(s):  
Antonio Elipe ◽  
Martín Lara
Keyword(s):  

2021 ◽  
Vol 33 (3) ◽  
pp. 037111
Author(s):  
Tianzhuang Xu ◽  
Jing Li ◽  
Zhihui Li ◽  
Shijun Liao
Keyword(s):  

Author(s):  
Hieu Nguyen ◽  
Hamzeh Bardaweel

The work presented here investigates a unique design platform for multi-stable energy harvesting using only interaction between magnets. A solid cylindrical magnet is levitated between two stationary magnets. Peripheral magnets are positioned around the casing of the energy harvester to create multiple stable positions. Upon external vibration, kinetic energy is converted into electric energy that is extracted using a coil wrapped around the casing of the harvester. A prototype of the multi-stable energy harvester is fabricated. Monostable and bistable configurations are demonstrated and fully characterized in static and dynamic modes. Compared to traditional multi-stable designs the harvester introduced in this work is compact, occupies less volume, and does not require complex circuitry normally needed for multi-stable harvesters involving piezoelectric elements. At 2.5g [m/s2], results from experiment show that the bistable harvester does not outperform the monostable harvester. At this level of acceleration, the bistable harvester exhibits intrawell motion away from jump frequency. Chaotic motion is observed in the bistable harvester when excited close to jump frequency. Interwell motion that yields high displacement amplitudes and velocities is absent at this acceleration.


2000 ◽  
Vol 11 (6) ◽  
pp. 923-928 ◽  
Author(s):  
P.H.A. Aragão ◽  
M. Simões

Author(s):  
A. Y. T. Leung ◽  
B. Ravindra ◽  
A. K. Mallik ◽  
C. W. Chan

Abstract Numerical simulations of the response of a harmonically excited mass on an isolator with a cubic, hard, non-linear restoring force and combined Coulomb and viscous damping are presented. For a base-excited system, the inclusion of a Coulomb damper with a suitable break-loose frequency can suppress the secondary resonances and chaotic motion. However, for a force-excited system, the introduction of Coulomb damping does not alter the bifurcation structure. Transmissibility indices have been defined for the solution obtained by numerical integration and the role of the subharmonic resonances and chaotic motion on the performance of the system is pointed out.


2021 ◽  
pp. 107754632110433
Author(s):  
Xiao-juan Wei ◽  
Ning-zhou Li ◽  
Wang-cai Ding

For the chaotic motion control of a vibro-impact system with clearance, the parameter feedback chaos control strategy based on the data-driven control method is presented in this article. The pseudo-partial-derivative is estimated on-line by using the input/output data of the controlled system so that the compact form dynamic linearization (CFDL) data model of the controlled system can be established. And then, the chaos controller is designed based on the CFDL data model of the controlled system. And the distance between two adjacent points on the Poincaré section is used as the judgment basis to guide the controller to output a small perturbation to adjust the damping coefficient of the controlled system, so the chaotic motion can be controlled to a periodic motion by dynamically and slightly adjusting the damping coefficient of the controlled system. In this method, the design of the controller is independent of the order of the controlled system and the structure of the mathematical model. Only the input/output data of the controlled system can be used to complete the design of the controller. In the simulation experiment, the effectiveness and feasibility of the proposed control method in this article are verified by simulation results.


1988 ◽  
Author(s):  
N. SRI NAMACHCHIVAYA ◽  
MONICA DOYLE
Keyword(s):  

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