Responses of infinite periodic structures to moving or stationary harmonic loads

Sheng, Xiaozhen; Jones, C.J.C.; Thompson, D.J.

doi:10.1016/j.jsv.2004.02.050

Cited by 121 publications

(86 citation statements)

References 13 publications

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“…Hence, this sequence converges to the solution of (17). By consequence, we can rebuild approximations of the response from (19) by using the sequence {c nk } when the value of k is large enough.…”

Section: Semi-analytical Methodsmentioning

confidence: 89%

“…The last equation defines a recurrent sequence {c nk } in k. If this sequence {c nk } converges to {c n }∀n when k → ∞, by replacing this series c nk , c n(k+1) by its limit c n , we find once again equation (17). Hence, this sequence converges to the solution of (17).…”

Section: Semi-analytical Methodsmentioning

confidence: 96%

“…We built series {c nk } such that c nk → c n when k, m → ∞ by inserting an evolution index k in equation (17). Such a series {c nk } is given by the following equations:…”

Section: Semi-analytical Methodsmentioning

confidence: 99%

“…In order to take into account the discrete supports, Mead [15,16] presented periodically supported beams for railway tracks. This model is also developed by other authors for different kind of linear supports and moving forces [17][18][19][20][21]. Although the analytical methods are well developed for linear cases, these methods can not be easily applied to nonlinear foundations.…”

Section: Introductionmentioning

confidence: 99%

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A Fast Semi-Analytical Method for Computing the Response of Railway Tracks on Nonlinear Foundations

Hoang¹,

Duhamel²,

Forêt³

et al. 2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The nonlinear vibration of railway tracks is a subject of some recent investigations. A main source of non-linearity comes from the railway foundations. For example, ballast and its lower layers or support systems of non-ballasted railway could have nonlinear behaviors. Models of beam under moving forces are often used for this dynamic system, and then the models are solved by numerical method or perturbation technique for some special nonlinear cases. This communication present a new method for calculating the response of railway tracks under moving trains loads. Based an analytical model of periodically supported beam, this model holds for all kinds of nonlinear foundations. Then, by using harmonic balance techniques and iteration procedures, a new method is developed to calculate the response of the model provided that the loading forces form a periodic impulse series. This kind of loading force represents charges of moving trains with equal mass wagons. This method is demonstrated to converge to the analytic solution of the model in case of linear foundation. Then, it is applied to bilinear and nonlinear foundation as examples. The results show that the nonlinear parameters of foundation have a strong influence on the railways track responses. This semi-analytical method is simple and could be efficient to compute the nonlinear vibrations of railway tracks.1

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Section: Semi-analytical Methodsmentioning

confidence: 89%

Section: Semi-analytical Methodsmentioning

confidence: 96%

“…We built series {c nk } such that c nk → c n when k, m → ∞ by inserting an evolution index k in equation (17). Such a series {c nk } is given by the following equations:…”

Section: Semi-analytical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Fast Semi-Analytical Method for Computing the Response of Railway Tracks on Nonlinear Foundations

Hoang¹,

Duhamel²,

Forêt³

et al. 2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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show abstract

“…In addition, the sleeper dynamic response is important because it affects the stability of the railway track and the maximum speed of the train. Substantial researches using analytic methods for rail track have been carried out, for example : the effect of wheel-rail contact forces [17,18] or the vibration of the railway track (by considering the model of a ballasted track with discrete supports [8,9,13,14,1] or the model of the infinite beam placed on a continuous foundation [10,7,6,11]). The studies of each component of the rail track were performed on the rail [19,16,15], or on the ballast [20,22].…”

Section: Introductionmentioning

confidence: 99%

Analytical Model of the Dynamics of Railway Sleeper

Tran¹,

Hoang²,

Forêt³

et al. 2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. The periodically supported beam is an analytical model of the dynamics of a railway track, where each rail together with its supports (sleepers) is independent of the other one. However, the sleepers connect the two rails and their behaviour could influence the response. This study develops an analytical model for this type of track by considering the sleepers as EulerBernoulli beams resting on a visco-elastic foundation. By using a relation between the reaction forces and displacement of the periodically supported beam [1], we can obtain a dynamic equation of a sleeper based on Dirac delta distribution. Then, the response of the sleepers can be obtained by using the Green function. This model is a fast method to calculate the dynamic responses of railway sleepers and track.

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A numerical model for foundation settlements due to deformation accumulation in granular soils under repeated small amplitude dynamic loading

François

Karg

Haegeman

et al. 2009

Num Anal Meth Geomechanics

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SUMMARYRepeated small amplitude dynamic loading of the soil in the vicinity of buildings, as arising from traffic or construction activities, may cause differential foundation settlements and structural damage. In this paper, a numerical model for soils under repeated dynamic loading is formulated. It is assumed that the dynamic part of the loading is small with respect to the static part, reflecting the stress conditions in the soil underneath buildings. As the plastic deformation in the soil is only observed after a considerable amount of dynamic loading cycles, only the accumulation of the average plastic deformation is considered. The model accounts for the dependency of the deformation on the stress conditions and the dynamic loading amplitude. The accumulation model is implemented in a finite element framework, using a consistent tangent approach in combination with a backward Euler integration scheme. A triaxial test is considered in a first numerical example. The available analytical solution for this problem allows to validate the numerical implementation. Second, the differential settlement of a two-storey building founded on loose sandy soil under repeated vehicle passages is considered. The differential foundation settlement causes the stresses to increase at the bottom of the wall, which may result in damage.

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Responses of infinite periodic structures to moving or stationary harmonic loads

Cited by 121 publications

References 13 publications

A Fast Semi-Analytical Method for Computing the Response of Railway Tracks on Nonlinear Foundations

A Fast Semi-Analytical Method for Computing the Response of Railway Tracks on Nonlinear Foundations

Analytical Model of the Dynamics of Railway Sleeper

A numerical model for foundation settlements due to deformation accumulation in granular soils under repeated small amplitude dynamic loading

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