Non-stationary random vibration analysis of three-dimensional train–bridge systems

This paper presents a new non-stationary random vibration technique for the analysis of three-dimensional, time-dependent, train–bridge systems that are subjected to excitations caused by track irregularities. It is based on the pseudo-excitation method (PEM), which was previously applicable only to time-invariant systems, but is extended herein and the result is strictly proven to be applicable to time-dependent systems. The analysis proceeds by taking time lags between the wheel excitations into account, in order that the effects of track irregularity can be regarded as a set of three-dimensional, uniformly modulated, multi-point, different-phase, non-stationary random excitations. This enables the random surface roughness of the track to be transformed using PEM into the superposition of a series of deterministic pseudo-harmonic surface irregularities. The precise integration method is then extended to compute the corresponding pseudo responses. By using these pseudo-responses, various non-stationary random responses, including the time-dependent PSD and RMS of the system, can be obtained conveniently and efficiently. Numerical examples show the effectiveness and accuracy of the present method by comparison with Monte Carlo simulation. Additionally, the characteristics of such non-stationary random responses are discussed.

[1]  Abimael F. D. Loula,et al.  Local gradient and stress recovery for triangular elements , 2002 .

[2]  M. B. Priestley,et al.  Power spectral analysis of non-stationary random processes , 1967 .

[3]  Yu-Kweng Michael Lin.  Probabilistic Theory of Structural Dynamics , 1976 .

[4]  H. Saunders,et al.  Introduction to Random Vibration , 1986 .

[5]  G. De Roeck,et al.  Dynamic analysis of train–bridge system and its application in steel girder reinforcement , 2001 .

[6]  J. G. S. da Silva.  Dynamical performance of highway bridge decks with irregular pavement surface , 2004 .

[7]  Jiahao Lin,et al.  Seismic Random Vibration of Long-Span Structures , 2005 .

[8]  Frederic Ward Williams,et al.  Seismic spatial effects for long-span bridges, using the pseudo excitation method , 2004 .

[9]  M. Kawatani,et al.  Dynamic response of a monorail steel bridge under a moving train , 2006 .

[10]  Zhang Ya-hui.  Wave passage effect on random seismic response of long-span structures , 2005 .

[11]  W X Zhong,et al.  DYNAMIC RESPONSE OF JACKET PLATFORM TO RANDOM WAVES , 1988 .

[12]  P. K. Chatterjee,et al.  Vibration of Continuous Bridges Under Moving Vehicles , 1994 .

[13]  W. Zhong.  Duality system in applied mechanics and optimal control , 2004 .

[14]  W. Zhong,et al.  A Precise Time Step Integration Method , 1994 .

[15]  L. G. Jaeger,et al.  Dynamics of structures , 1990 .

[16]  Nan Zhang,et al.  Dynamic analysis of railway bridge under high-speed trains , 2005 .

[17]  L Fryba,et al.  VIBRATION OF SOLIDS AND STRUCTURES UNDER MOVING LOADS (3RD EDITION) , 1999 .

[18]  Francis T.K. Au,et al.  Effects of random road surface roughness and long-term deflection of prestressed concrete girder and cable-stayed bridges on impact due to moving vehicles , 2001 .

[19]  Y. K. Cheung,et al.  Impact study of cable-stayed railway bridges with random rail irregularities , 2002 .

[20]  S. D. Xue,et al.  Nonstationary response of spatial lattice shells under multiple seismic inputs , 2002 .

[21]  Chang-Koon Choi,et al.  A new three-dimensional finite element analysis model of high-speed train–bridge interactions , 2003 .