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.

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.

CONTROLLING CHAOS IN A STATE-DEPENDENT NONLINEAR SYSTEM

2002 ◽  
Vol 12 (05) ◽  
pp. 1111-1119 ◽  
Author(s):  
TAKUJI KOUSAKA ◽  
TETSUSHI UETA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
Dynamical System ◽  
Nonlinear System ◽  
Periodic Orbits ◽  
Chaotic Attractor ◽  
Discrete System ◽  
Nonlinear Dynamical System ◽  
Nonlinear Dynamical ◽  
Controlling Chaos ◽  
State Dependent ◽  
General Method

In this paper, we propose a general method for controlling chaos in a nonlinear dynamical system containing a state-dependent switch. The pole assignment for the corresponding discrete system derived from such a nonsmooth system via Poincaré mapping works effectively. As an illustrative example, we consider controlling the chaos in the Rayleigh-type oscillator with a state-dependent switch, which is changed by the hysteresis comparator. The unstable one- and two-periodic orbits in the chaotic attractor are stabilized in both numerical and experimental simulations.

scholarly journals Dual Faceted Linearization of Nonlinear Dynamical Systems Based on Physical Modeling Theory

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
H. Harry Asada ◽  
Filippos E. Sotiropoulos
Keyword(s):  
Dynamical System ◽  
Nonlinear System ◽  
Differential Equations ◽  
Physical Modeling ◽  
Nonlinear Dynamical System ◽  
State Variables ◽  
Auxiliary Variables ◽  
State Equations ◽  
Nonlinear Dynamical ◽  
Modeling Theory

A new approach to modeling and linearization of nonlinear lumped-parameter systems based on physical modeling theory and a data-driven statistical method is presented. A nonlinear dynamical system is represented with two sets of differential equations in an augmented space consisting of independent state variables and auxiliary variables that are nonlinearly related to the state variables. It is shown that the state equation of a nonlinear dynamical system having a bond graph model of integral causality is linear, if the space is augmented by using the output variables of all the nonlinear elements as auxiliary variables. The dynamic transition of the auxiliary variables is investigated as the second set of differential equations, which is linearized by using statistical linearization. It is shown that the linear differential equations of the auxiliary variables inform behaviors of the original nonlinear system that the first set of state equations alone cannot represent. The linearization based on the two sets of linear state equations, termed dual faceted linearization (DFL), can capture diverse facets of the nonlinear dynamics and, thereby, provide a richer representation of the nonlinear system. The two state equations are also integrated into a single latent model consisting of all significant modes with no collinearity. Finally, numerical examples verify and demonstrate the effectiveness of the new methodology.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

DYNAMICAL ESTIMATION OF CALENDAR EFFECTS

2006 ◽  
Vol 06 (01) ◽  
pp. L7-L15
Author(s):  
ALEXANDROS LEONTITSIS
Keyword(s):  
Dynamical System ◽  
Time Series ◽  
Noise Level ◽  
Nonlinear Dynamical System ◽  
Main Tool ◽  
Experimental Results ◽  
Accurate Estimation ◽  
Nonlinear Dynamical ◽  
Correlation Integral ◽  
Calendar Effects

The paper introduces a method for estimation and reduction of calendar effects from time series, which their fluctuations are governed by a nonlinear dynamical system and additive normal noise. Calendar effects can be considered deviations of the distribution(s) of particular group(s) of observations that have a common characteristic related to the calendar. The concept of this method is the following: since the calendar effects are not related to the dynamics of the time series, the accurate estimation and reduction will result a time series with a smaller amount of noise level (i.e. more accurate dynamics). The main tool of this method is the correlation integral, due to its inherit capability of modeling both the dynamics and the additive normal noise. Experimental results are presented on the Nasdaq Cmp. index.

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