Nonlinear dynamics of multicomponent three-dimensional systems of noncanonical form

1988 ◽  
Vol 24 (7) ◽  
pp. 717-722
Author(s):  
M. A. Pavlovskii ◽  
Yu. V. Radysh ◽  
A. S. Kireev
Keyword(s):  
Nonlinear Dynamics ◽  
Three Dimensional ◽  
Noncanonical Form

Nonlinear Dynamics and Application of the Four Dimensional Autonomous Hyper-Chaotic System

2014 ◽  
Author(s):  
Ge Kai ◽  
Wei Zhang
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Simulation ◽  
Differential Equations ◽  
Chaotic System ◽  
Dynamical Behavior ◽  
Three Dimensional ◽  
Phase Portraits ◽  
State Variables ◽  
Chaotic Motions ◽  
Finance System

In this paper, we establish a dynamic model of the hyper-chaotic finance system which is composed of four sub-blocks: production, money, stock and labor force. We use four first-order differential equations to describe the time variations of four state variables which are the interest rate, the investment demand, the price exponent and the average profit margin. The hyper-chaotic finance system has simplified the system of four dimensional autonomous differential equations. According to four dimensional differential equations, numerical simulations are carried out to find the nonlinear dynamics characteristic of the system. From numerical simulation, we obtain the three dimensional phase portraits that show the nonlinear response of the hyper-chaotic finance system. From the results of numerical simulation, it is found that there exist periodic motions and chaotic motions under specific conditions. In addition, it is observed that the parameter of the saving has significant influence on the nonlinear dynamical behavior of the four dimensional autonomous hyper-chaotic system.

Three-Dimensional Nonlinear Dynamics of Cold Atoms in an Optical Lattice and its Realizations

2021 ◽  
Vol 42 (5) ◽  
pp. 558-568
Author(s):  
Sergey V. Prants ◽  
Leonid E. Kon’kov ◽  
Aleksandr A. Didov
Keyword(s):  
Nonlinear Dynamics ◽  
Optical Lattice ◽  
Cold Atoms ◽  
Three Dimensional

scholarly journals Nonlinear dynamics in three-dimensional QED and nontrivial infrared structure

1999 ◽  
Vol 60 (12) ◽  
Author(s):  
N. E. Mavromatos ◽  
J. Papavassiliou
Keyword(s):  
Nonlinear Dynamics ◽  
Three Dimensional

Nonlinear dynamics of three-dimensional vortex-induced vibration prediction model for a flexible fluid-conveying pipe

2018 ◽  
Vol 138-139 ◽  
pp. 99-109 ◽  
Author(s):  
Wenwu Yang ◽  
Zhijiu Ai ◽  
Xiaodong Zhang ◽  
Xueping Chang ◽  
Ruyi Gou
Keyword(s):  
Nonlinear Dynamics ◽  
Prediction Model ◽  
Three Dimensional ◽  
Vortex Induced Vibration ◽  
Vibration Prediction

A Nonlinear Dynamics Analysis of Vortex-Structure Interaction Models

2001 ◽  
Vol 123 (4) ◽  
pp. 475-479 ◽  
Author(s):  
N. W. Mureithi ◽  
S. Goda ◽  
H. Kanki ◽  
T. Nakamura
Keyword(s):  
Nonlinear Dynamics ◽  
Parameter Space ◽  
Vortex Structure ◽  
Three Dimensional ◽  
Order Model ◽  
Third Order ◽  
Interaction Models ◽  
Structure Interaction ◽  
Lock In ◽  
Fifth Order

Vortex-structure interaction models are studied in the work presented here. The third- order model by Hartlen and Currie (HC model) can reproduce the correct response amplitude, while a fifth-order model by Landl predicts the observed hysterisis effect. Using concepts from nonlinear dynamics and bifurcation theory, the range of possible dynamics of the models is investigated in parameter space; essentially, a class of nonlinear oscillators deriving “naturally” from the HC model is studied. It is found that perturbations of the HC model in parameter space lead to qualitatively physically meaningful dynamics. Forced excitation of the HC model is the highlight of the work. In this case, it is shown that a subharmonic lock-in predicted by the model may be related to a three-dimensional secondary subharmonic instability of a periodic flow. Experimental results are presented for comparison.

Nonlinear dynamics of three-dimensional long-wave Marangoni instability in thin liquid films

2000 ◽  
Vol 12 (7) ◽  
pp. 1633-1645 ◽  
Author(s):  
Alexander Oron
Keyword(s):  
Nonlinear Dynamics ◽  
Three Dimensional ◽  
Liquid Films ◽  
Thin Liquid Films ◽  
Marangoni Instability ◽  
Long Wave

A Hybrid Rod-Catenary Model to Simulate Nonlinear Dynamics of Cables With Low and High Tension Zones

2005 ◽  
Author(s):  
S. Goyal ◽  
N. C. Perkins
Keyword(s):  
Nonlinear Dynamics ◽  
Three Dimensional ◽  
Computational Effort ◽  
Integration Time ◽  
Computationally Efficient ◽  
High Tension ◽  
Rod Model ◽  
Marine Cable ◽  
Low Tension ◽  
Nonlinear Deformations

Cables under very low tension may become highly contorted and form loops, tangles, knots and kinks. These nonlinear deformations, which are dominated by flexure and torsion, pose serious concerns for cable deployment. Simulation of the three-dimensional nonlinear dynamics of loop and tangle formation requires a 12th order rod model and the computational effort increases rapidly with increasing cable length and integration time. However, marine cable applications which result in local zones of low-tension very frequently involve large zones of high-tension where the effects of flexure and torsion are insignificant. Simulation of the three-dimensional dynamics of high-tension cables requires only a 6th order catenary model which significantly reduces computational effort relative to a rod model. We propose herein a hybrid computational cable model that employs computationally efficient catenary elements in high-tension zones and rod elements in localized low-tension zones to capture flexure and torsion precisely where needed.

scholarly journals Campbell Diagram Computation for a Drillstring Immersed in Curved Wells

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Khac-Long Nguyen ◽  
Quang-Thinh Tran ◽  
Marie-Ange Andrianoely ◽  
Lionel Manin ◽  
Régis Dufour ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Three Dimensional ◽  
Element Formulation ◽  
Fluid Structure Interactions ◽  
Flexural Mode ◽  
Stick Slip ◽  
Campbell Diagram ◽  
Contact Points ◽  
Modal Coupling ◽  
Drilling Operations

The drilling operations use a rotary slender structure introduced inside the drill well. The nonlinear dynamics with bit-bouncing, stick-slip phenomena, and pulsating mud flow may yield the premature wear and damage of drilling equipment and should be investigated to improve the reliability of drilling operations. This work presents the beam element formulation to model the drilling nonlinear dynamics. The well-pipe contacts are modeled by the radial elastic stops. The fluid–structure interactions are considered. The first step consists in computing the static position of structure to determine the contact points and calculate the preloaded state. These results are then considered to calculate the Campbell diagram. The potentially unstable speeds of rotation are identified. The results show that the modal coupling phenomena strongly occur for the three-dimensional well. The well-pipe contacts modify the modes in rotation, and the rotating fluid induces a strong deviation of the flexural mode curves.

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