The Stability and Chaos Analysis of a Nonlinear Wheeled Vehicle Model Under Road Excitation

2010 ◽  
Author(s):  
Hamed Samandari ◽  
Mousa Rezaee
Keyword(s):  
Dynamical Behavior ◽  
Great Influence ◽  
Surface Profile ◽  
Degree Of Freedom ◽  
The Road ◽  
Roughness Amplitude ◽  
Road Excitation ◽  
Quarter Car ◽  
The Stability ◽  
Unsprung Mass

In this paper, the dynamic behavior of a quarter-car with two degree-of-freedom which consists of sprung mass and unsprung mass is examined. Nonlinearity occurred due to nonlinear hysteretic suspension damper and spring. Vehicle tire is modeled as a nonlinear hardening spring. The disturbance of road assumed to be sinusoid. Frequency response diagram of the model has been obtained. Results show that the dynamic response of the vehicle can be chaotic. Influence of road roughness amplitude on vehicle vibration is investigated and critical amplitude of the road surface profile is found, above which the system can vibrate chaotically. The comparison between the results obtained from the proposed model and those from the single degree-of-freedom quarter-car model shows that the unsprung mass has great influence on the dynamical behavior of the system, which cannot be ignored.

scholarly journals Dynamic modeling and analysis of vertical vibration reduction system for passenger train

Mechanika ◽  
2021 ◽  
Vol 27 (5) ◽  
pp. 415-420
Author(s):  
Shichang Dong ◽  
Hao Song ◽  
Caiyun Song
Keyword(s):  
Dynamical Behavior ◽  
Vibration Reduction ◽  
Vertical Vibration ◽  
The Body ◽  
Degree Of Freedom ◽  
Modeling And Analysis ◽  
Impact System ◽  
Reduction System ◽  
Train Operation ◽  
The Stability

Based on wheel-rail impact vibration and considering the body stiffness and natural damping, this paper builds a four-degree-of-freedom vibro-impact system model for passenger train’s vertical vibration reduction system. The Poincaré map of the system is determined by the analytic solution of the system derived from the motion differential equation of the multi-degree-of-freedom vibro-impact system combined with Newton's second law. It is found that the fork bifurcation, Hopf bifurcation and other dynamical behavior leading to Chaos when the system parameters are changed. On this basis, the dynamic parameters of the train are optimized to avoid chaos in the train operation, reduce the vertical vibration of the train, improve the stability and comfort of the train operation, and provide the theoretical basis for the active vibration reduction design of the train.

scholarly journals Chaotic vibration of a quarter-car model excited by the road surface profile

2008 ◽  
Vol 13 (7) ◽  
pp. 1373-1383 ◽  
Author(s):  
Grzegorz Litak ◽  
Marek Borowiec ◽  
Michael I. Friswell ◽  
Kazimierz Szabelski
Keyword(s):  
Surface Profile ◽  
Road Surface ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Chaotic Vibration ◽  
Quarter Car

scholarly journals State Estimation Based on Sigma Point Kalman Filter for Suspension System in Presence of Road Excitation Influenced by Velocity of the Car

2019 ◽  
Vol 2019 ◽  
pp. 1-16 ◽  
Author(s):  
Chi Nguyen Van
Keyword(s):  
Kalman Filter ◽  
State Estimation ◽  
Ride Comfort ◽  
Suspension System ◽  
Wheel Load ◽  
The Road ◽  
Sigma Point ◽  
Road Excitation ◽  
On The Road ◽  
Unsprung Mass

The states of the suspension system including the road excitation depend on the road quality, the velocity of the car, and the sprung mass. Those states play a very important role in the control problem of stability, ride comfort, ride safety, and dynamic wheel load of the suspension systems. The velocities and deflections of the sprung mass and unsprung mass would not be measured fully in the practice. Therefore, it must be estimated by other measured quantities from the system such as acceleration and deflection of sprung mass and unsprung mass. To control the active suspension system, its states need to be estimated accurately and guaranteed the response time. This paper presents the method using the sigma point Kalman filter to estimate the suspension system’s states including the road excitation, the deflections, and the velocities of the sprung mass and unsprung mass. The mathematical model of the suspension system is rewritten for the state estimation problem, and the stochastic load profile is supposed the main noise input. The stochastic characteristic of the road excitation depending on the car’s velocity is taken into account in the model used for suspension system state estimation. The results calculated based on the practical experiment data for specific road profile with some particular velocities of the car show that the suspension system states are estimated quite accurately in comparison with the practice states.

Numerical Stability Analysis of a Forced Two-D.O.F. Oscillator With Bilinear Damping

2007 ◽  
Vol 2 (3) ◽  
pp. 211-217 ◽  
Author(s):  
Zsolt Szabó ◽  
Attila Lukács
Keyword(s):  
Degrees Of Freedom ◽  
Governing Equations ◽  
Vehicle Model ◽  
Pseudorandom Sequences ◽  
First Order ◽  
The Road ◽  
Damping Behavior ◽  
Numerical Stability Analysis ◽  
Road Excitation ◽  
The Stability

The current paper investigates the nonlinear stationary oscillations of a quarter vehicle model with two degrees of freedom subjected to a vertical road excitation. The damping of the wheel suspension has a bilinear characteristic, so that the damping strength is larger during compression than during restitution of the damper. For the optimization of the damping behavior the peak-to-peak swings have to be as small as possible. The unevenness of the road was approximated by filtered white noise which was modelled numerically using pseudorandom sequences. The first order form of the governing equations was transformed to hyperspherical representation. The stability was determined according to the largest Liapunov exponents obtained from the numerical simulation. For a chosen parameter range stability charts were constructed both in the stochastic and harmonic case (for comparison).

Nonlinear vibration of a quarter-car model excited by the road surface profile

PAMM ◽  
2008 ◽  
Vol 8 (1) ◽  
pp. 10893-10894 ◽  
Author(s):  
Grzegorz Litak ◽  
Marek Borowiec
Keyword(s):  
Nonlinear Vibration ◽  
Surface Profile ◽  
Road Surface ◽  
The Road ◽  
Quarter Car Model ◽  
Car Model ◽  
Quarter Car

scholarly journals Nonlinear Dynamics Analysis of the Semiactive Suspension System with Magneto-Rheological Damper

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Hailong Zhang ◽  
Enrong Wang ◽  
Fuhong Min ◽  
Ning Zhang ◽  
Chunyi Su ◽  
...  
Keyword(s):  
Dynamical Behavior ◽  
Period Doubling ◽  
Suspension System ◽  
Nonlinear Stability Analysis ◽  
Chaotic Motions ◽  
The Road ◽  
Road Profile ◽  
Road Excitation ◽  
Magneto Rheological ◽  
Period Doubling Bifurcations

This paper examines dynamical behavior of a nonlinear oscillator which models a quarter-car forced by the road profile. The magneto-rheological (MR) suspension system has been established, by employing the modified Bouc-Wen force-velocity (F-v) model of magneto-rheological damper (MRD). The possibility of chaotic motions in MR suspension is discovered by employing the method of nonlinear stability analysis. With the bifurcation diagrams and corresponding Lyapunov exponent (LE) spectrum diagrams detected through numerical calculation, we can observe the complex dynamical behaviors and oscillating mechanism of alternating periodic oscillations, quasiperiodic oscillations, and chaotic oscillations with different profiles of road excitation, as well as the dynamical evolutions to chaos through period-doubling bifurcations, saddle-node bifurcations, and reverse period-doubling bifurcations.

scholarly journals Online Classification of Road Roughness Conditions with Vehicle Unsprung Mass Acceleration by Sliding Time Window

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Zhongxing Li ◽  
Wenhao Yu ◽  
Xiaoli Cui
Keyword(s):  
Time Window ◽  
Vehicle Speed ◽  
The Road ◽  
Physical Measurements ◽  
Online Classification ◽  
Power Spectral ◽  
Road Roughness ◽  
The Stability ◽  
Roughness Classification ◽  
Unsprung Mass

Suspension control systems are in need for more information of road roughness conditions to improve their performance under different roads. Existing methods of gauging road roughness are limited, and they usually involve visual inspections or special vehicles equipped with instruments that can gauge physical measurements of road irregularities. This paper proposes data collection for a period of a time from accelerometers fixed on unsprung mass and uses the mean square values of this datasets divided by vehicle speed to classify the roughness conditions of a section of a road. This approach is possible due to the existence of relationships between the power spectral densities of the road surface, unsprung mass accelerations via a transfer function, and vehicle speed. This paper gave the relationship between the resolution of road roughness classification and the length of time-window and suggestions about choosing the appropriate time-window length on the balance of road roughness resolution and classification delay. Moreover, to enhance the stability of classification, the influence of damping parameters of vehicle suspension on the classification output is studied, and a classification method of road roughness is proposed based on neural network and damping coefficient correction.

scholarly journals Dynamic Behaviors and the Equivalent Realization of a Novel Fractional-Order Memristor-Based Chaotic Circuit

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Ningning Yang ◽  
Cheng Xu ◽  
Chaojun Wu ◽  
Rong Jia ◽  
Chongxin Liu
Keyword(s):  
Numerical Simulations ◽  
Dynamic Behavior ◽  
Fractional Order ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Great Influence ◽  
Equivalent Circuits ◽  
Chaotic Circuit ◽  
Undetermined Coefficient ◽  
The Stability

This paper proposed a novel fractional-order memristor-based chaotic circuit. A memristive diode bridge cascaded with a fractional-order RL filter constitutes the generalized fractional-order memristor. The mathematical model of the proposed fractional-order chaotic circuit is established by extending the nonlinear capacitor and inductor in the memristive chaotic circuit to the fractional order. Detailed theoretical analysis and numerical simulations are carried out on the dynamic behavior of the proposed circuit by investigating the stability of equilibrium points and the influence of circuit parameters on bifurcations. The results show that the order of the fractional-order circuit has a great influence on the dynamical behavior of the system. The system may exhibit complicated nonlinear dynamic behavior such as bifurcation and chaos with the change of the order. The equivalent circuits of the fractional-order inductor and capacitor are also given in the paper, and the parameters of the equivalent circuits are solved by an undetermined coefficient method. Circuit simulations of the equivalent fractional-order memristive chaotic circuit are carried out in order to validate the correctness of numerical simulations and the practicability of using the integer-order equivalent circuit to substitute the fractional-order element.

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