Symplectic analysis of vertical random vibration for coupled vehicle–track systems

Lü, Feng; Kennedy, David; Williams, F.W.; Lin, J. H.

doi:10.1016/j.jsv.2008.03.004

Cited by 64 publications

(37 citation statements)

References 12 publications

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“…In many traditional dynamic analysis models, the vehicle system is regarded as a multi-rigid-body system [3,4,11]. In recent years, many scholars [15][16][17][18] have studied the effect of an elastic car body on the vibration of a vehicletrack coupled system.…”

Section: Frequency Analysis Methods For the Vehicle-track Vertical Coumentioning

confidence: 99%

“…The stiffness matrixes P a and P b of neighboring substructures can be obtained from the symplectic characteristics of the transfer matrix of unstressed substructures [11]. Inserting the stiffness matrixes P a and P b into Eq.…”

Section: Equation Of Motion Of the Track Systemmentioning

confidence: 99%

“…To improve the efficiency of computation, Lin and Zhang [10] put forward a pseudoexcitation method. The pseudo-excitation method was then adopted by Lu et al [11] and Zhang et al [12,13] to analyze the vertical random vibration of a vehicle-track coupled system. This method regards the track structure as a periodic structure and solves the spreading of harmonic virtual track irregularity excitation in the track substructure with a symplectic mathematics method.…”

Section: Introductionmentioning

confidence: 99%

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Distribution characteristics and influencing factors of the frequency-domain response of a vehicle–track vertical coupled system

Wang

et al. 2016

J. Mod. Transport.

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Employing theory on vehicle-track coupled dynamics, the equation of motion of a vehicle-track vertical coupled system was established by combining frequency analysis and symplectic mathematics. The frequency response of the vehicle-track vertical coupled system was calculated under the excitation of the German low-interference spectrum, and the effects of the vehicle speed, vehicle suspension parameters, and track support parameters on the frequency response of the coupled system were studied. Results show that, under the excitation of the German lowinterference spectrum, the vertical vibration of the car body is mainly concentrated in the low-frequency band, while that of the bogie has a wide frequency distribution, being strong from several Hertz to dozens of Hertz. The vertical vibrations of the wheel-rail force, wheelset, and track structure mainly occur at a frequency of dozens of Hertz. In general, the vertical vibration of the vehicle-track coupled system increases with vehicle speed, and the vertical vibrations of the car body and bogie obviously shift to higher frequency. Increasing the vehicle suspension stiffness increases the lowfrequency vibrations of the vehicle system and track structure. With an increase in vehicle suspension damping, the low-frequency vibrations of the car body and bogie and the vibrations of the wheel-rail vertical force and track structure decrease at 50-80 Hz, while the mid-frequency and highfrequency vibrations of the car body and bogie increase. Similarly, an increase in track stiffness amplifies the vertical vibrations of the wheel-rail force and track structure, while an increase in track damping effectively reduces the vertical vibrations of the wheel-rail vertical force and track structure.

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Section: Frequency Analysis Methods For the Vehicle-track Vertical Coumentioning

confidence: 99%

Section: Equation Of Motion Of the Track Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Distribution characteristics and influencing factors of the frequency-domain response of a vehicle–track vertical coupled system

Wang

et al. 2016

J. Mod. Transport.

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“…Lin et al [14,15] combined the SMM with the PEM to solve for stationary/non-stationary random wave propagation in damped periodic structures. Lu et al [16] then applied Lin's method to calculate the stationary random response of the coupled vehicle-track dynamic system.…”

Section: Introductionmentioning

confidence: 99%

Identification of the power spectral density of vertical track irregularities based on inverse pseudo-excitation method and symplectic mathematical method

Zhang¹,

Zhao

Zhang

et al. 2013

Inverse Problems in Science and Engineering

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A new method is proposed to identify the power spectral density (PSD) of vertical track irregularities. A vertical coupled vehicle-track dynamic model is established. In this model, a vehicle is simplified as a multi-rigid-body model with 10 degrees of freedom, and a track is treated as a three-layer discrete elastic support model in which the rail, which is supported discretely by the sleepers, is described by Bernoulli-Euler beam theory. The vehicle and track models are coupled by a linearized Hertzian spring. The axle box acceleration is selected as the measurement data, and the stationary PSD of the axle box acceleration is simply transformed into its displacement PSD. The PSD of the vertical track irregularities is identified using a combination of the inverse pseudo-excitation method and the symplectic mathematical method. The accuracy of the proposed method is investigated for the different measurement noise levels, vehicle speeds, primary suspension parameters and PSD classes. The numerical results indicate that the proposed method can accurately identify the PSD of the vertical track irregularities.

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“…Some detailed models have been developed that consider the coupling of vehicles and railway track [1][2][3][4]. These studies have focused on the dynamic interaction of the track and vehicle using non-linear Hertzian spring elements.…”

Section: Introductionmentioning

confidence: 99%

The Influence of Subgrade Subsidence on Train Track Dynamic Interaction

O’Brien¹,

Taheri²,

Gavin³

Civil-Comp Proceedings

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This paper reports results from a numerical model to calculate subgrade settlement in railway tracks due to repeated dynamic loading. The trains are modelled as rigid body 2-axle carriages on two layers of springs. The track is modelled as a beam supported on three layers of springs. Permanent deformation of the subgrade layer is calculated on the basis of a power law assumption. Patterns of dynamic forces are calculated on a smooth track and on a track subject to an initial subgrade 'pothole'. The latter is shown to grow with repeated loading and to change the mean patterns of applied force.

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Symplectic analysis of vertical random vibration for coupled vehicle–track systems

Cited by 64 publications

References 12 publications

Distribution characteristics and influencing factors of the frequency-domain response of a vehicle–track vertical coupled system

Distribution characteristics and influencing factors of the frequency-domain response of a vehicle–track vertical coupled system

Identification of the power spectral density of vertical track irregularities based on inverse pseudo-excitation method and symplectic mathematical method

The Influence of Subgrade Subsidence on Train Track Dynamic Interaction

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