TAILIEUCHUNG - Transition length of two stationary random functions in investigation of railway stability

In this paper the scientific justification for determination of transition length of two stationary random functions is presented on the basis of the weight function and properties of stationary random function in wide sense. | Vietnam Journal of Mechanics, NCST of Vietnam Vol. 22, 2000, No 1 (47 - 53) · . TRANSITION LENGTH OF TWO STATIONARY RANDOM FUNCTIONS IN INVESTIGATION OF RAILWAY STABILITY NGUYEN DUONG NAM Research institute for transportation science and technology ABSTRACT. In this paper the scientific justification for determination of transition length of two stationary random functions is presented on the basis of the weight function and properties of stationary random function in wide sense. The application of the results for practice gives the transition lengths of straight and curved railway, which it is necessary to throw away in measurement of initial horizontal displacement of railway in its stability estimation under action of longitudinal compression load. STRAIGHT SEGMENT 1. Introduction Measurement data of the initial horizontal displacement of the neutral axis of straight and curved railway are different stationary gaussian random functions. The connection of the two kinds of the railway makes them to become unstationary, and it is difficult for processing measurement data for research of railway To overcome the difficulty it is necessary to find the reasona~le set of measurement data near to connection place, which must be no used in its processing. The problem will be solved below by theory and application in practice. 47 2. Scientific justification . Let us consider the mechanical system governed by random differential equation Fxy(x) = HxYo(x), () where () and aj (j = O, . . . , n), bk (k = 0, . , m) are real constant coefficients, y 0 (x) is input random function of independent variable x, y(x) is output function. 'rhe mean value my(x) and variance Dy(x) of y(x) can be found by the following formulae [2J J x my(x) = my 0 W(x, s)ds = my0 h(x), () 0 x Dy(x) where my 0 = a~(x) = = const x J J 0 0 W(x, §i) [ W(x, s2)Ky0 (s1 - s2)ds2 Jds1, () is mean value of input stationary random function .

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• Transition length of two stationary random functions
• Investigation of railway stability
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• Dang Dinh Ang
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