Dynamics of a Pumping System

2016 ◽  
Vol 823 ◽  
pp. 85-90
Author(s):  
Nicolae Dumitru ◽  
Dan B. Marghitu ◽  
Nicolae Craciunoiu
Keyword(s):  
Angular Velocity ◽  
Dynamic Stability ◽  
Lyapunov Exponents ◽  
Chaotic Motion ◽  
Phase Plane ◽  
Elastic Displacement ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Pumping System ◽  
Largest Lyapunov Exponents

In this paper a pumping systems for deep extraction is simulated using SolidWorks and ADAMS. The elastic displacement of a point on the flexible moving cable is analyzed. The dynamics of the system is characterized with phase plane, Poincaré maps, and Lyapunov exponents. The Lyapunovexponents represent the dynamic stability of the system. The largest Lyapunov exponents for three different angular velocity show the chaotic motion of the system

Observation and Evolution of Chaos for an Autonomous System

1984 ◽  
Vol 51 (3) ◽  
pp. 664-673 ◽  
Author(s):  
E. H. Dowell
Keyword(s):  
Elastic Plate ◽  
Physical Interpretation ◽  
Autonomous System ◽  
Phase Plane ◽  
Power Spectra ◽  
Poincaré Maps ◽  
Flowing Fluid ◽  
Poincare Maps ◽  
Time Histories

Time histories, phase plane portraits, power spectra, and Poincare maps are used as descriptors to observe the evolution of chaos in an autonomous system. Although the motions of such a system can be quite complex, these descriptors prove helpful in detecting the essential structure of the motion. Here the principal interest is in phase plane portraits and Poincare maps, their methods of construction, and physical interpretation. The system chosen for study has been previously discussed in the literature, i.e., the flutter of a buckled elastic plate in a flowing fluid.

Chaotic Motion of a Nonhomogeneous Torsional Pendulum

1997 ◽  
Vol 07 (03) ◽  
pp. 733-740 ◽  
Author(s):  
Jiin-Po Yeh
Keyword(s):  
Total Energy ◽  
Lyapunov Exponents ◽  
Chaotic Motion ◽  
Local Minimum ◽  
Phase Plane ◽  
Nonlinear Oscillations ◽  
Initial Conditions ◽  
Chaotic Motions ◽  
Torsional Pendulum ◽  
Damped Systems

In this paper, the nonlinear oscillations of a nonhomogeneous torsional pendulum are investigated. Chaotic motions are shown to exist in both damped systems with two-well potential and undamped systems with one-well or two-well potential. Autocorrelations of the Poincaré mappings of the motion are presented and shown to be another useful tool to judge whether the system is chaotic. The total energy of the torsional pendulum is explored as well and it is conjectured that the irregularity of the total energy is probably one of the important factors which cause chaos. Lyapunov exponents are used as an indication of chaos in this paper. For systems with two-well potential, the phase-plane trajectories are found to stay in one well if the motion is regular, but jump from one well to another if the motion is chaotic. Making the initial conditions near the local minimum of the two-well potential is proved to be successful in preventing chaos from happening in the undamped systems.

Nonlinear Analysis of Temperature during Orthogonal Turning

2018 ◽  
Vol 880 ◽  
pp. 309-314
Author(s):  
Nicolae Craciunoiu ◽  
Dan B. Marghitu ◽  
Nicolae Dumitru ◽  
Adrian Sorin Rosca
Keyword(s):  
Nonlinear Dynamics ◽  
Time Delay ◽  
Lyapunov Exponents ◽  
Phase Plane ◽  
Chaotic Behavior ◽  
Stability Index ◽  
Depth Of Cut ◽  
Embedding Dimension ◽  
Orthogonal Turning ◽  
Largest Lyapunov Exponents

In this paper orthogonal turning processes are analyzed for different depth of cut. The temperature during the machining is analyzed. The nonlinear dynamics of the orthogonal turning are characterized with fft, phase plane, time delay, embedding dimension and largest Lyapunov exponents. The Lyapunov exponents can be used as a dynamic stability index for the system. The largest Lyapunov exponents for two different depth of cut show the chaotic behavior of the system.

Presenting joint kinematics of human locomotion using phase plane portraits and Poincaré maps

1994 ◽  
Vol 27 (12) ◽  
pp. 1495-1499 ◽  
Author(s):  
Yildirim Hurmuzlu ◽  
Cagatay Basdogan ◽  
James J. Carollo
Keyword(s):  
Phase Plane ◽  
Human Locomotion ◽  
Joint Kinematics ◽  
Poincaré Maps ◽  
Poincare Maps

STRANGE NONCHAOTIC ATTRACTORS FROM PERIODICALLY EXCITED CHUA'S CIRCUIT

2001 ◽  
Vol 11 (01) ◽  
pp. 225-230 ◽  
Author(s):  
ZHONG LIU
Keyword(s):  
Lyapunov Exponents ◽  
Chua’S Circuit ◽  
Poincaré Maps ◽  
Chua's Circuit ◽  
Poincare Maps ◽  
Strange Nonchaotic Attractors ◽  
Singular Continuous Spectra

In this paper, we discuss the existence of strange nonchaotic attractors for the Chua's circuit with periodical excitation. We have studied the Lyapunov exponents, Poincaré maps, singular continuous spectra of characterizing the attractors. The results show that the excited Chua's circuit does indeed have the strange nonchaotic behaviors.

Analysis of Bifurcations and Chaos in Three Coupled Physical Pendulums With Impacts

2001 ◽  
Author(s):  
Jan Awrejcewicz ◽  
Grzegorz Kudra ◽  
C.-H. Lamarque
Keyword(s):  
Lyapunov Exponents ◽  
Discontinuity Point ◽  
Basins Of Attraction ◽  
External Forcing ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Transition Condition ◽  
Triple Pendulum ◽  
Linearized System

Abstract In this work the triple pendulum with damping, external forcing and with impacts is investigated. The extension of a coefficient restitution rule and a special transition condition rule for perturbation (linearized system in the Lyapunov exponents algorithm) in each discontinuity point are applied. Periodic, quasi-periodic, chaotic and hyperchaotic motions are observed using Poincaré maps and bifurcational diagrams, which are verified by the Lyapunov exponents. In additon basins of attraction of some coexisting regular and irregular attractors are illustrated and discussed.

Strange Nonchaotic Attractors of Chua's Circuit with Quasiperiodic Excitation

1997 ◽  
Vol 07 (01) ◽  
pp. 227-238 ◽  
Author(s):  
Zhiwen Zhu ◽  
Zhong Liu
Keyword(s):  
Lyapunov Exponents ◽  
Period Doubling ◽  
Period Doubling Bifurcation ◽  
Smooth Transition ◽  
Chua’S Circuit ◽  
Poincaré Maps ◽  
Strange Nonchaotic Attractor ◽  
Chua's Circuit ◽  
Poincare Maps ◽  
Strange Nonchaotic Attractors

This paper focuses attention on strange nonchaotic attractor of Chua's circuit with two-frequency quasiperiodic excitation. Existence of the attractor is confirmed by calculating several characterizing quantities such as Lyapunov exponents, Poincaré maps, double Poincaré maps and so on. Two basic mechanisms are described for the development of the strange nonchaotic attractor from two-frequency quasiperiodic state (torus solution). One of them is torus-doubling bifurcation followed by a smooth transition from the torus attractor to the strange nonchaotic attractor; and another is that the torus does not undergo period-doubling bifurcation at all; instead, the torus attractor gradually becomes wrinkled, and eventually becomes strange but nonchaotic.

Dynamic Stability of Vehicle Systems via Poincaré Maps

1997 ◽  
Vol 28 (1) ◽  
pp. 41-55
Author(s):  
DAN B. MARGHITU ◽  
DAVID G. BEALE ◽  
S.C. SINHA
Keyword(s):  
Dynamic Stability ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Vehicle Systems

Chaotic Motion of an Elastic-Plastic Beam

1988 ◽  
Vol 55 (1) ◽  
pp. 185-189 ◽  
Author(s):  
B. Poddar ◽  
F. C. Moon ◽  
S. Mukherjee
Keyword(s):  
Finite Element ◽  
Transient Response ◽  
Chaotic Motion ◽  
Solid Mechanics ◽  
Numerical Study ◽  
Periodic Excitation ◽  
Poincaré Maps ◽  
Poincare Maps ◽  
Elastic Plastic ◽  
Extreme Sensitivity

A numerical study is presented here which suggests that chaotic motion is possible from periodic excitation of an elastic-plastic beam. Poincare´ maps of the motion reveal a fractal-like structure of the attractor. The results suggest that geometric and material nonlinearities in solid mechanics problems may lead to extreme sensitivity to small changes in parameters and resulting unpredictability. These results may explain the total disagreement of nine finite element codes in the analysis of the transient response of an elastic-plastic beam, that has been reported recently by Symonds and his coworkers.

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