Dynamic response of infinite continuous beams subjected to a moving force—An exact method

Cai, Chao; Cheung, Y.K.; Chan, H. P.

doi:10.1016/s0022-460x(88)80163-9

Cited by 71 publications

(33 citation statements)

References 5 publications

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“…Warburton [7] analytically investigated the same problem and found that the maximum dynamic ampliÿcation in de ection occurred for a speciÿc speed of the moving load. Cai et al [8] solved the problem of the moving load on an inÿnite uniform beam on periodic roller supports, by also employing mode superposition. Very recently, Chen and Huang [9] considered a constant load moving at constant velocity along an inÿnite Timoshenko beam on viscoelastic foundation.…”

Section: Introductionmentioning

confidence: 99%

Moving element method for train‐track dynamics

Koh

Ong

Chua

et al. 2003

Numerical Meth Engineering

129

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SUMMARYThis paper presents a new approach, called the moving element method, for the dynamic analysis of train-track systems. By discretizing the rail beam on viscoelastic foundation into elements that ' ow' with the moving vehicle, the proposed method eliminates the need for keeping track of the vehicle position with respect to the track model. The governing equations are formulated in a co-ordinate system travelling at a constant velocity, and a class of conceptual elements (as opposed to physical elements) are derived for the rail beams. In the numerical study, four cases of moving vehicle are presented taking into consideration the e ects of moving load and rail corrugation. The method is shown to work for varying vehicle velocity and multiple contact points, and has several advantages over the ÿnite element method. The numerical solutions compare favourably with the results obtained by alternative methods.

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Section: Introductionmentioning

confidence: 99%

Moving element method for train‐track dynamics

Koh

Ong

Chua

et al. 2003

Numerical Meth Engineering

129

View full text Add to dashboard Cite

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“…By using the Newmark direct integration method [22], one may obtain the values of +q(t),, +qR (t), and +qK (t), from equation (17). The vector for the vertical (transverse) THE DYNAMIC ANALYSIS OF A MULTISPAN FLUID-CONVEYING PIPE displacements of the piping system at any time t, +y(t),, is then determined by…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…In Refs. [17,18], the order of the overall property matrices for the whole multispan structure is signi"cantly reduced by using the dynamic sti!ness matrices [19] and only one element per span. However, the order of the overall property matrices for the whole structure is yet to increase with the number of spans.…”

Section: Introductionmentioning

confidence: 99%

“…This is unlike the transfer matrix method (TMM) [16,20], in which the order of the overall transfer matrix is kept unchanged. Furthermore, since the dynamic responses obtained from the dynamic-sti!ness-matrix method are in the &&frequency domain'' [17,18], the last method will not be a suitable approach if the pertinent information required is the dynamic responses in the &&time domain'' such as the time histories of displacements for certain points of a piping system.…”

Section: Introductionmentioning

confidence: 99%

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The Dynamic Analysis of a Multispan Fluid-Conveying Pipe Subjected to External Load

Wu¹,

Shih²

2001

Journal of Sound and Vibration

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“…A simple class of periodic structures is the so-called rotationally periodic structures, that is described in the pioneer publication [2]. Their dynamic behaviour has been studied in the publication [3] and extended to infinite spatially periodic structures by Cal et al [4], using a method, equivalent to the one presented by Thomas, called U-transform. The static analysis of spatially periodic structures has been studied by Cheung et al [5] applying the ideas of U-transform.…”

mentioning

confidence: 99%

Analysis of the railway track as a spatially periodic structure

García‐Palacios

Samartín

Melis

2011

Proceedings of the Institution of Mechanical Engineers, Part F:

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This article presents a new and computationally efficient method of analysis of a railway track modelled as a continuous beam of 2N spans supported by elastic vertical springs. The main feature of this method is its important reduction in computational effort with respect to standard matrix methods of structurai anaiysis. In this article, the whole structure is considered to be a repetition of a single one. The analysis presented is applied to a simple railway track model, Le. to a repetitive beam supported on vertical springs (sleepers). The proposed method of analysis is based on the general theory of spatially periodic structures. The main feature of this theory is the possibility to apply Discrete Fourier Transform (OFT) in order to reduce a large system of q(2N + I) linear stiffness equilibrium equations to a set of 2N+ I uncoupled systems of q equations each. In this way, a dramatic reduction of the computational effort of solving the large system of equations is achieved. This fact is particularly important in the analysis of railway track structures, in which N is a very large number (around several thousands), and q= 2, the verticai displacement and rotation, is very small. The proposed method allows us to easily obtain the exact solution given by Samartin [1], Le. the continuous beam railway track response. The comparison between the proposed method and other methods of anaiysis of railway tracks, such as Lorente de No and Zimmermann-Timoshenko, clearly shows the accuracy of the obtained results for the proposed method, even for low values of N In addition, identicai results between the proposed and the Lorente methods have been found, although the proposed method seems to be of simpler application and computationally more efficient than the Lorente one. Smail but significative differences occur between these two methods and the one developed by Zimmermann-Timoshenko. This article aiso presents a detailed sensitivity anaiysis of the verticai displacement of the sleepers. Although standard matrix methods of structurai analysis can handle this railway model, one of the objectives of this article is to show the efficiency of OFT method with respect to standard matrix structural anaiysis. A comparative analysis between standard matrix structurai analysis and the proposed method (OFT), in terms of computationai time, input, output and aiso software programming, will be carried out. Finaily, a URL link to a MatLab computer program list, based on the proposed method, is given

show abstract

Dynamic response of infinite continuous beams subjected to a moving force—An exact method

Cited by 71 publications

References 5 publications

Moving element method for train‐track dynamics

Moving element method for train‐track dynamics

The Dynamic Analysis of a Multispan Fluid-Conveying Pipe Subjected to External Load

Analysis of the railway track as a spatially periodic structure

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