Chaotic Motion of Axial Loaded Beam Bridge Subjected to an Infinite Series of Moving Loads

2013 ◽  
Vol 470 ◽  
pp. 1024-1027
Author(s):  
Li Feng Du ◽  
Xin Wei Yang ◽  
Jun Jun Li
Keyword(s):  
Nonlinear System ◽  
Infinite Series ◽  
Integral Inequality ◽  
Chaotic Motion ◽  
Infinite Sequence ◽  
Pulse Excitation ◽  
Approximation Methods ◽  
Moving Loads ◽  
Beam Bridge ◽  
Novel Model

We presented a novel model which comprises an axial loaded beam bridge subjected to an infinite series of regularly spaced concentrated moving loads. The axial force coupled with the moving loads can lead the vibration of the beam bridge to chaos that drive the system of a given basin and jump to another one, causing damage due to the resulting amplitude jumps. An infinite sequence of moving loads leads to a barrier for conventional nonlinear techniques. The amplification and minification of integral inequality are proposed, which lead to the criteria for chaotic motion directly for the nonlinear system with a half sine pulse excitation avoiding the conventional approximation methods to retain the nature characteristics of the system. The results show the chaotic motion takes place in the system.

Chaotic Threshold for Axial Loaded Beam Bridge under Moving Loads

2014 ◽  
Vol 533 ◽  
pp. 140-144
Author(s):  
Shi Zhu Yang ◽  
Xin Wei Yang
Keyword(s):  
Dynamical System ◽  
Nonlinear System ◽  
Chaotic Motion ◽  
Nonlinear Dynamical System ◽  
Pulse Excitation ◽  
Approximation Methods ◽  
Moving Loads ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
Beam Bridge

We studied chaotic threshold of a nonlinear dynamical system of beam bridge. The amplification and minification of integral inequality are proposed, which lead to the criteria for chaotic motion directly for the nonlinear system with a half sine pulse excitation avoiding the conventional approximation methods to retain the nature characteristics of the system. The efficiency of the criteria for chaotic motion obtained by use of the Melnikov's method is verified via the bifurcation diagrams, Lyapunov exponents and numerical simulations.

scholarly journals Vibration reduction in beam bridge under moving loads using nonlinear smooth and discontinuous oscillator

2016 ◽  
Vol 8 (6) ◽  
pp. 168781401665256 ◽  
Author(s):  
Ruilan Tian ◽  
Xinwei Yang ◽  
Qin Zhang ◽  
Xiuying Guo
Keyword(s):  
Vibration Reduction ◽  
Moving Loads ◽  
Beam Bridge ◽  
Nonlinear Smooth

Investigation on Dynamics of the Extended Duffing-Van der Pol System

2009 ◽  
Vol 64 (5-6) ◽  
pp. 341-346 ◽  
Author(s):  
Jun Yu ◽  
Jieru Li
Keyword(s):  
Numerical Simulation ◽  
Fractal Dimension ◽  
Nonlinear System ◽  
Computer Simulations ◽  
Chaotic Motion ◽  
Dynamical Behaviour ◽  
Higher Order ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Melnikov Analysis

Abstract The chaotic motion in periodic self-excited oscillators has been extensively investigated through experiments and computer simulations. However, with the advent of the study of chaotic motion by means of strange attractors, Poincar´e map, fractal dimension, it has become necessary to seek for a better understanding of nonlinear system with higher order nonlinear terms. In this paper we consider an extended Duffing-Van der Pol oscillator by introducing a nonlinear quintic term. The dynamical behaviour of the system is investigated by using Melnikov analysis and numerical simulation. The results can help one to understand the essence of given nonlinear system.

THE STUDY ON THE MIDSPAN DEFLECTION OF A BEAM BRIDGE UNDER MOVING LOADS BASED ON SD OSCILLATOR

2012 ◽  
Vol 22 (05) ◽  
pp. 1250108 ◽  
Author(s):  
R. L. TIAN ◽  
X. W. YANG ◽  
Q. J. CAO ◽  
Y. W. HAN
Keyword(s):  
Moving Loads ◽  
External Excitation ◽  
Response Curves ◽  
First Order ◽  
Sd Oscillator ◽  
Driven System ◽  
Complete Elliptic Integrals ◽  
Beam Bridge ◽  
Nonlinear Behaviors ◽  
Midspan Deflection

In this paper, the midspan deflection of a beam bridge with vehicles passing through the bridge successively is investigated. The midspan deflection can be modeled as the vibration trace of smooth-and-discontinuous (SD) oscillator by considering the mode of the first order and up-and-down vibration. The nonlinear behaviors of the established model are studied and presented. KAM (Kolmogorov–Arnold–Moser) structures on the Poincaré section are constructed for the driven system without dissipation with generic KAM curve and a series of resonant points and the surrounding island chains connected by chaotic orbits. Introducing a series of complete elliptic integrals of the first and the second kind, the response curves of the system are detected, to which the effects of parameters are revealed. The relevant dynamics is depicted under external excitation exhibiting period leading to chaos. The efficiency of the bifurcation diagrams obtained in this paper is demonstrated via numerical simulations.

scholarly journals Chaotic Motion in Forced Duffing System Subject to Linear and Nonlinear Damping

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Tai-Ping Chang
Keyword(s):  
Lyapunov Exponent ◽  
Nonlinear System ◽  
Chaotic Motion ◽  
Chaotic Behavior ◽  
Duffing Oscillator ◽  
Nonlinear Damping ◽  
Critical Value ◽  
Duffing System ◽  
Linear And Nonlinear

This paper investigates the chaotic motion in forced Duffing oscillator due to linear and nonlinear damping by using Melnikov technique. In particular, the critical value of the forcing amplitude of the nonlinear system is calculated by Melnikov technique. Further, the top Lyapunov exponent of the nonlinear system is evaluated by Wolf’s algorithm to determine whether the chaotic phenomenon of the nonlinear system actually occurs. It is concluded that the chaotic motion of the nonlinear system occurs when the forcing amplitude exceeds the critical value, and the linear and nonlinear damping can generate pronounced effects on the chaotic behavior of the forced Duffing oscillator.

Periodic and Chaotic Motion of a Time-Delayed Nonlinear System Under Two Coexisting Families of Additive Resonances

2017 ◽  
Vol 27 (05) ◽  
pp. 1750066 ◽  
Author(s):  
J. C. Ji ◽  
Terry Brown
Keyword(s):  
Hopf Bifurcation ◽  
Nonlinear System ◽  
Periodic Motion ◽  
Chaotic Motion ◽  
Forced Response ◽  
Phase Portraits ◽  
Frequency Spectra ◽  
Nonlinear Mechanical ◽  
Nonlinear Mechanical System ◽  
Delayed System

A time-delayed quadratic nonlinear mechanical system can exhibit two coexisting stable bifurcating solutions (SBSs) after two-to-one resonant Hopf bifurcations occur in the corresponding autonomous time-delayed system. One SBS is of small-amplitude and has the Hopf bifurcation frequencies (HBFs), while the other is of large-amplitude and contains the shifted Hopf bifurcation frequencies (the shifted HBFs). When the forcing frequency is tuned to be the sum of two HBFs or the sum of two shifted HBFs, two families of additive resonances can be induced in the forced response. The forced response under the additive resonance related to the HBFs can demonstrate periodic, quasi-periodic and chaotic motion. On the contrary, the forced response under the additive resonance associated with the shifted HBFs may exhibit period-three periodic motion and quasi-periodic motion. Bifurcation diagrams, time trajectories, frequency spectra, phase portraits and Poincaré sections are presented to show periodic, quasi-periodic, and chaotic motion of the time-delayed nonlinear system under the two families of additive resonances.

CHAOTIC BEHAVIOR IN A FRACTIONAL-ORDER SYSTEM CONTAINING A CONTINUOUS ORDER-DISTRIBUTION

2012 ◽  
Vol 22 (10) ◽  
pp. 1250253 ◽  
Author(s):  
TOM T. HARTLEY ◽  
CARL F. LORENZO
Keyword(s):  
Nonlinear System ◽  
Fractional Order ◽  
Function Method ◽  
Chaotic Behavior ◽  
Order System ◽  
Fractional Dynamics ◽  
Approximation Methods ◽  
Describing Function ◽  
Describing Function Method ◽  
Bifurcation Behavior

This paper discusses the fractional dynamics, and the bifurcation behavior, of a specific nonlinear system that contains a continuous order-distribution. The dynamics of the system are predicted using the describing-function method. General approximation methods are then derived for the continuous order-distribution component. The system is simulated using these approximations, and the results compared with the describing-function predictions. This is believed to be the first observation of chaos in a system with continuous order-distribution.

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