Instability of a Bogie Moving on a Flexibly Supported Timoshenko Beam

Verichev, Stanislav; Metrikine, Andrei V.

doi:10.1006/jsvi.2001.4069

Cited by 30 publications

(13 citation statements)

References 16 publications

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“…Analytical solutions for complex problems are not explicit. For example, Metrikine et al [8,9,14] adopted the D-decomposition method to graphically identify a root with a positive real part for the stability problems of an axially compressed beam on a Kelvin foundation under a moving mass and the stability problems of an EB beam on a Kelvin foundation subjected to two oscillators and a four-degrees-of-freedom (DOF) bogie. Chen et al [15,16] employed the dynamic stiffness matrix method to investigate the vibration of a Timoshenko beam on a Kelvin foundation subjected to a moving concentrated load and a concentrated harmonic load.…”

Section: Introductionmentioning

confidence: 99%

“…The beam-foundation system can be used as an idealization of the interaction of rail tracks and subsoil or pavements and subgrades, wherein the rail track or pavement is simplified as a Euler-Bernoulli (EB) [1][2][3][4][5][6][7][8][9][10][11], Rayleigh [12], shear [13], Timoshenko [14][15][16][17], or laminated composite beam [18,19]; and the subsoil or subgrade is idealized as a Winkler [7,10], Kelvin [1- 6,8,9,[11][12][13][14][15][16], or Pasternak foundation [17][18][19]. This topic has attracted increasing attention because super-high-speed and super-high-capacity vehicles nowadays are being widely adopted as mass transportation carriers in many countries [6].…”

Section: Introductionmentioning

confidence: 99%

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Vibration of Timoshenko beam on hysteretically damped elastic foundation subjected to moving load

Luo

Xia

Weng

2015

Sci. China Phys. Mech. Astron.

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The vibration of beams on foundations under moving loads has many applications in several fields, such as pavements in highways or rails in railways. However, most of the current studies only consider the energy dissipation mechanism of the foundation through viscous behavior; this assumption is unrealistic for soils. The shear rigidity and radius of gyration of the beam are also usually excluded. Therefore, this study investigates the vibration of an infinite Timoshenko beam resting on a hysteretically damped elastic foundation under a moving load with constant or harmonic amplitude. The governing differential equations of motion are formulated on the basis of the Hamilton principle and Timoshenko beam theory, and are then transformed into two algebraic equations through a double Fourier transform with respect to moving space and time. Beam deflection is obtained by inverse fast Fourier transform. The solution is verified through comparison with the closed-form solution of an Euler-Bernoulli beam on a Winkler foundation. Numerical examples are used to investigate: (a) the effect of the spatial distribution of the load, and (b) the effects of the beam properties on the deflected shape, maximum displacement, critical frequency, and critical velocity. These findings can serve as references for the performance and safety assessment of railway and highway structures. vibration, beam-foundation system, moving load PACS number(s): 02.30.Nw, 46.70.De, 46.40.-Ff, 45.20.Jj Citation:Luo W L, Xia Y, Weng S. Vibration of Timoshenko beam on hysteretically damped elastic foundation subjected to moving load.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Vibration of Timoshenko beam on hysteretically damped elastic foundation subjected to moving load

Luo

Xia

Weng

2015

Sci. China Phys. Mech. Astron.

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“…Finally, it has to be mentioned that the problem of instability of a moving oscillator along an infinite beam on viscoelastic foundation has already been studied extensively by many authors, in particular, Verichev and Metrikine [23]. They have used very similar models and also the D-decomposition method, to calculate the critical velocity and to map the stable/unstable ranges in the parameters' space of the oscillator.…”

Section: Discussionmentioning

confidence: 98%

“…The issue of the unstable response of different kinds of moving subsystems and elastic structures modeling the railway vehicle/track system has been studied in many papers, beginning in Denisov et al [19] and Bogacz et al [20] and continuing to the studies developed by Metrikine and Verichev [21], Verichev [22], Verichev and Metrikine [23], Wolfert et al [24], and Zheng and Fan [25]. The main goal of all these studies is to identify the instability regions in the parameters' space of the systems considered.…”

Section: Introductionmentioning

confidence: 99%

Instability of an oscillator moving along a Timoshenko beam on viscoelastic foundation

2011

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The paper herein presents an analysis of the vibration instability phenomenon of a three-mass oscillator that is uniformly moving along a continuously viscoelastic supported Timoshenko beam, due to the anomalous Doppler waves excited in the beam. Such phenomenon may appear in the case of railway trains crossing areas with soft soil when the train velocity exceeds the phase velocity of the waves induced in the track structure. The model proposed here corresponds to a two-level suspension vehicle running on a track and it includes the wheel/rail contact nonlinearities (the Hertzian contact characteristic and the possibility of contact loss). First, the velocities at the stability limit are calculated by means of the D-decomposition method via a new form of the characteristic equation based on the receptances; the characteristic equation has been obtained using the Green's function of the differential operator of the Laplace transformed equations of motion. Therefore, the stability map including two stability/instability zones has been determined. Secondly, the time-domain analysis of the dynamic behavior due to the stability loss has been performed by solving the equations of motion in virtue of the convolution theorem. The previously determined velocities at the stability limit have been confirmed via the time-T. Mazilu ( ) · M. Dumitriu · C. Tudorache Department of Railway Vehicles, University Politehnica of Bucharest 313, domain analysis applied to the linear approximation of the equations of motion. Thirdly, the limit cycle characterizing the unstable motion is analyzed. This takes the form of successive shocks, exhibiting a very high magnitude of the contact force, especially in the case of the velocities within the second unstable zone.

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“…Super-high-speed and super-high-capacity vehicles nowadays are increasingly adopted as land transportation carriers. Their safety becomes a public concern when the vehicle speed exceeds the critical velocity of the road–soil system or when the load frequency approaches the critical frequency of the system (Metrikine and Dieterman, 1997; Verichev and Metrikine, 2002; Wolfert et al, 1998). In this regard, the model of beams on elastic or viscoelastic foundations has drawn wide attention, in which the beam and foundation are reasonable idealizations of the road and soil, respectively.…”

Section: Introductionmentioning

confidence: 99%

Vibration of infinite Timoshenko beam on Pasternak foundation under vehicular load

Luo

Xia

2017

Advances in Structural Engineering

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The vibration of beams on foundations under a vehicular load has attracted wide attention for decades. The problem has numerous applications in several fields such as highway structures. However, most of analytical or semi-analytical studies simplify the vehicular load as a concentrated point or distributed line load with the constant or harmonically varying amplitude, and neglect the presence of the vehicle and the road irregularity. This article carries out an analytical study of vibration on an infinite Pasternak-supported Timoshenko beam under vehicular load which is generated by the passage of a quarter car on a road with harmonic surface irregularity. The governing equations of motion are derived based on Hamilton’s principle and Timoshenko beam theory and then are solved in the frequency–wavenumber domain with a moving coordinate system. The analytical solutions are expressed in a general form of Cauchy’s residue theorem. The results are validated by the case of an Euler–Bernoulli beam on a Winkler foundation, which is a special case of the current system and has an explicit form of solution. Finally, a numerical example is employed to investigate the influence of properties of the beam (the radius of gyration and the shear rigidity) and the foundation (the shear viscosity, rocking, and normal stiffness) on the deflected shape, maximum displacement, critical frequency, and critical velocity of the system.

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Instability of a Bogie Moving on a Flexibly Supported Timoshenko Beam

Cited by 30 publications

References 16 publications

Vibration of Timoshenko beam on hysteretically damped elastic foundation subjected to moving load

Vibration of Timoshenko beam on hysteretically damped elastic foundation subjected to moving load

Instability of an oscillator moving along a Timoshenko beam on viscoelastic foundation

Vibration of infinite Timoshenko beam on Pasternak foundation under vehicular load

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