Chaotic response of a quarter car model forced by a road profile with a stochastic component

Litak, Grzegorz; Borowiec, Marek; Friswell, Michael I.; Przystupa, Wojciech

doi:10.1016/j.chaos.2007.07.021

Cited by 45 publications

(29 citation statements)

References 25 publications

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“…Blue and red lines belong to the damping values D = .105 and D = 0.72, respectively. Note that for vanishing excitation bandwidth δ = 0, the related mean square car response (12) coincides with the resonance diagram of cars riding on harmonic wave road surfaces. For stochastic roads δ > 0, the induced vertical car vibrations vanish for infinitely increasing speeds and there are no magnifications when the car slows down; i.e.…”

Section: Quarter Cars Riding On Rough Random Roadsmentioning

confidence: 63%

“…models of a quarter car with asymmetric piecewise linear damping are considered. In [12], the influence of cubic damping and restoring characteristics are investigated for car models excited by a road profile with harmonic and stochastic components. Both papers are restricted to the nonlinear across dynamics of quarter car models under the assumption of so-called frozen base excitations by road profiles which allow no investigations of transient or fluctuating car velocities.…”

Section: Quarter Cars Riding On Rough Random Roadsmentioning

confidence: 99%

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Jump phenomena in road-vehicle dynamics

Wedig

2015

Int. J. Dynam. Control

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Provided that vehicles are riding with constant velocity, the mean value of the car driving force needed to compensate energy dissipation through the wheel damping, is calculated. For suitably strong harmonic road excitations, there are two stable and one unstable velocity near the critical speed of the car. This behavior is extended to the case of stochastic roads that shows corresponding effects when the calculated mean driving force is plotted versus the constant car velocity. More important is the inverse case that the driving force of the car is fixed by means of a suitable control meanwhile the car velocity is variable and fluctuates around a stationary mean value. For small car damping and narrowbanded road profile, a further acceleration of under-critical car velocities is no longer possible because of the blockade by the resonance characteristic. The car velocity finally jumps to much higher speeds when the driving force is strongly reinforced in order to pass over the resonance peak. This behavior is investigated for stochastic road profiles described by new second order filter equations under additive white noise applied to the across and along dynamics of quarter car models. To clarify main original contributions, this paper presents first investigations of the along dynamics of quarter car models applying a new nonlinear first order car equation which is strongly coupled through randomly fluctuating car velocities with the second order road and car equations of the vertical road and car displacements, respectively. The associated systematic behavior is numerically investigated by means of covariance equations showing jump phenomena of B Walter V. Wedig the mean car velocity that corresponds to the Sommerfeld effect, well-known in rotor dynamics.

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Section: Quarter Cars Riding On Rough Random Roadsmentioning

confidence: 63%

Section: Quarter Cars Riding On Rough Random Roadsmentioning

confidence: 99%

Jump phenomena in road-vehicle dynamics

Wedig

2015

Int. J. Dynam. Control

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“…In recent years, many studies have developed these phenomena in a variety of vehicle models with various degrees of freedom. Litak et al [12][13][14] investigated chaotic vibrations in a quarter-car model with one degree of freedom under the sinusoidal excitation force of road. The stability and chaos analyses of a nonlinear quarter-vehicle model with two degrees of freedom were investigated by Samandari and Rezaee [15].…”

Section: Introductionmentioning

confidence: 99%

Chaotic behaviors of a ground vehicle oscillating system with passengers

2017

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Abstract. In this paper, some considerations regarding a ground vehicle oscillating system based on chaotic behaviors are studied. The vehicle system is modeled as a full nonlinear seven-degree freedom with an additional degree of freedom for each passenger. Roughness of the road surface is considered as sinusoidal waveforms with time delays for the tires. The governing di erential equations are extracted under Newton-Euler laws and solved via numerical methods. The dynamic behavior of the system is investigated by special nonlinear techniques such as bifurcation diagram, time series, phase plane portrait, power spectrum, Poincar e section, and maximum Lyapunov exponents. The time delays between the tires are used as a control parameter. First, the vehicle behavior is investigated and the chaotic regions are detected. Then, the damping and sti ness coe cients are used to return to the regular behavior. Results show that by changing the system parameters and selecting the appropriate values, one can minimize vibrations as well as eliminate chaotic behavior. The comparison of the results obtained from the proposed model and those from the vehicle without passengers show the great di erences in the dynamic behaviors of the two models.

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“…15 Litak et al investigated the chaotic motion in a hysteresis nonlinear vehicle suspension system which subjected to multi-frequency excitation, and found the critical amplitude of the road surface when the system vibrates chaotically. [16][17][18] Naik et al established the limited conditions of operation of the MR damper in vehicle suspension systems. Chaotic motion was indicated by bifurcation diagram and the Lyapunov exponent (LE).…”

Section: Introductionmentioning

confidence: 99%

Bifurcations and chaos of a vibration isolation system with magneto-rheological damper

Zhang

Min

et al. 2016

AIP Advances

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Magneto-rheological (MR) damper possesses inherent hysteretic characteristics. We investigate the resulting nonlinear behaviors of a two degree-of-freedom (2-DoF) MR vibration isolation system under harmonic external excitation. A MR damper is identified by employing the modified Bouc-wen hysteresis model. By numerical simulation, we characterize the nonlinear dynamic evolution of period-doubling, saddle node bifurcating and inverse period-doubling using bifurcation diagrams of variations in frequency with a fixed amplitude of the harmonic excitation. The strength of chaos is determined by the Lyapunov exponent (LE) spectrum. Semi-physical experiment on the 2-DoF MR vibration isolation system is proposed. We trace the time history and phase trajectory under certain values of frequency of the harmonic excitation to verify the nonlinear dynamical evolution of period-doubling bifurcations to chaos. The largest LEs computed with the experimental data are also presented, confirming the chaotic motion in the experiment. We validate the chaotic motion caused by the hysteresis of the MR damper, and show the transitions between distinct regimes of stable motion and chaotic motion of the 2-DoF MR vibration isolation system for variations in frequency of external excitation.

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Chaotic response of a quarter car model forced by a road profile with a stochastic component

Cited by 45 publications

References 25 publications

Jump phenomena in road-vehicle dynamics

Jump phenomena in road-vehicle dynamics

Chaotic behaviors of a ground vehicle oscillating system with passengers

Bifurcations and chaos of a vibration isolation system with magneto-rheological damper

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