Dynamic response of a finite beam resting on a Winkler foundation to a load moving on its surface with variable speed

Beskou, Niki D.; Muho, Edmond V.

doi:10.1016/j.soildyn.2018.02.033

Cited by 22 publications

(11 citation statements)

References 10 publications

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“…Due to viscoelastic nature of asphalt material, it is well known that mechanical responses of asphalt pavement under moving vehicular loading are affected by tire-pavement interaction and speed [6,7]. Analytical solutions of viscoelastic pavement responses vary with different levels of complexity depending on the assumptions of pavement structure (such as finite beam, infinite plate on Winkler foundation, or multiple layers) and moving loads (constant, harmonic, or random loads) [3,4,[8][9][10][11][12]. e solutions can be closed-form solutions in analytical form based on the corresponding principle or semianalytical form solved using numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

Prediction of Viscoelastic Pavement Responses under Moving Load and Nonuniform Tire Contact Stresses Using 2.5-D Finite Element Method

Wang

Zhao

et al. 2020

Mathematical Problems in Engineering

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This study developed two-and-half dimensional (2.5-D) finite element method (FEM) to predict viscoelastic pavement responses under moving loads and nonuniform tire contact stresses. The accuracy of 2.5-D FEM was validated with two analytical solutions for elastic and viscoelastic conditions. Compared to three-dimensional (3-D) FEM, the computational efficiency of the 2.5-D method was greatly improved. The effects of loading pattern and speed on pavement surface deflection and strain responses were analyzed for asphalt pavements with four different asphalt layer thicknesses. The analyzed pavement responses included surface deflections, maximum tensile strains in the asphalt layer, and maximum compressive strains on top of subgrade. The loading patterns have influence on the mechanical responses. According to the equivalent rule, the point load, rectangle type, and sinusoid-shape contact stresses were studied. It was found that the point load caused much greater pavement responses than that of the area-based loading. When the tire loading was simplified as uniform contact stress in rectangular area, the maximum tensile strains in the asphalt layer varied with the width/length ratio of contact area. Additionally, it was shown that the dynamic responses of pavement structure induced by the sinusoid-shape contact stresses and realistic nonuniform stresses were quite similar to each other in all the cases. The pavement strain responses decreased as the speed increased due to viscoelastic behavior of asphalt layer. The study results indicate that asphalt pavement responses under moving load can be calculated using the proposed 2.5-D FEM in a fast manner for mechanistic-empirical pavement design and analysis.

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Section: Introductionmentioning

confidence: 99%

Prediction of Viscoelastic Pavement Responses under Moving Load and Nonuniform Tire Contact Stresses Using 2.5-D Finite Element Method

Wang

Zhao

et al. 2020

Mathematical Problems in Engineering

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“…If the effects of the shear deformation and the rotational inertia in the beam are neglected, the EB beam theory can be applied to the dynamic analysis. [1][2][3][4][5][6][7][8] Based on the EB beam theory, Timoshenko 9 developed a physically more rigorous theory taking account of the influence of the shear deformation and the rotational inertia in the beam. The vibrations of a Timoshenko beam supported by a foundation were then investigated.…”

Section: Introductionmentioning

confidence: 99%

“…The foundations of the problem are considered as discrete springs or a half-space comprising continuous medium. The discrete spring model includes a Winkler 4,6,[10][11][12][13][15][16][17] and a Pasternak type foundation. 5,7,8,14,18 This kind of model facilitates the derivation of the closed-form solutions, but it cannot present the wave coupling of the foundation and superstructure.…”

Section: Introductionmentioning

confidence: 99%

Moving load response of an axially loaded Timoshenko beam on a multilayered transversely isotropic half‐space comprising different media

Feng

Chen

2020

Num Anal Meth Geomechanics

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This paper investigates the dynamic response of an axially loaded Timoshenko beam coupled with a multilayered transversely isotropic (TI) half-space subjected to a moving load. An axial force induced by the thermal expansion is taken into account in the Timoshenko beam. The half-space considers the alternate distribution of an arbitrary number of TI elastic and poroelastic layers to model foundation soils with different properties and moisture conditions. To solve the governing equations, Fourier transform is adopted. The stratified foundation is formulated by extending an "adapted stiffness matrix method" to a more general scenario with an arbitrary number of layers. The beam is then coupled with the foundation to derive solutions to the system in the frequency-wavenumber domain. The final results in the time-spatial domain are recovered by the inverse Fourier transform. After confirming the accuracy of the method in this study, the influences of the pore water existence, the transverse isotropy of different parameters, and the axial force are investigated. It can be observed that the effect of pore water existence on the maximum beam deflection can reach 22% in this study. The transverse isotropy of the elastic and shear moduli influences the critical speed of the beam deflection by altering the phase velocity of the first wave propagation mode of the beam-foundation system. The vertical permeability coefficient is more important than the horizontal one in determining the excess pore pressure. The rise of the beam temperature (axial force) decreases the critical speed and magnifies the vibrations.

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“…If we consider it as a planar model, it can be reduced to a two-axle model. In the field of vehicle-bridge coupling system, many researchers studied the dynamic responses of bridges/beams subjected to moving vehicles with two axles [9][10][11]. In these papers, vehicles are in contact with the beams through two wheels, and the assumed mode method is adopted to derive the deflections of the beams.…”

Section: Introductionmentioning

confidence: 99%

“…In these papers, vehicles are in contact with the beams through two wheels, and the assumed mode method is adopted to derive the deflections of the beams. Inspired by [9][10][11], we proposed a novel moving load model for 2D crane systems of which the trolley has two axles. is new model can provide more accurate results of the dynamic responses of the crane beam.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of a Gantry Crane’s Beam Subjected to a Two-Axle Moving Trolley

Chen

Gao

et al. 2020

Mathematical Problems in Engineering

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In this paper, a novel moving load model for 2D crane systems of which the trolley has two axles is proposed. Based on this model, the dynamics of a 2D gantry crane, which is modelled as a simply supported Euler–Bernoulli beam carrying a two-axle trolley from which a single-pendulum payload is suspended, is studied. The proposed model was verified by comparing with two models in existing papers and can be considered as an extended version of comparative models. Then, the effect of the trolley’s axle base on the dynamic responses of the beam is studied. It can be observed that increasing the length of trolley’s axle base will decrease the deflection of the beam, and a larger initial swing angle will cause a larger deflection of the beam without controlling the swing of the payload.

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Dynamic response of a finite beam resting on a Winkler foundation to a load moving on its surface with variable speed

Cited by 22 publications

References 10 publications

Prediction of Viscoelastic Pavement Responses under Moving Load and Nonuniform Tire Contact Stresses Using 2.5-D Finite Element Method

Prediction of Viscoelastic Pavement Responses under Moving Load and Nonuniform Tire Contact Stresses Using 2.5-D Finite Element Method

Moving load response of an axially loaded Timoshenko beam on a multilayered transversely isotropic half‐space comprising different media

Dynamic Response of a Gantry Crane’s Beam Subjected to a Two-Axle Moving Trolley

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