The non-stationary freefield response for a moving load with a random amplitude

This paper presents a stochastic solution procedure for the calculation of the non-stationary freefield response due to a moving load with a random amplitude. In this case, a non-stationary autocorrelation function and a time-dependent spectral density are required to characterize the response at a fixed point in the freefield. The non-stationary solution is derived from the solution in the case of a moving load with a deterministic amplitude. It is shown how the deterministic solution can be calculated in an efficient way by means of integral transformation methods if the problem geometry exhibits a translational invariance in the direction of the moving load. A key ingredient is the transfer function between the source and the receiver that represents the fundamental response in the freefield due to an impulse load at a fixed location. The solution in the case of a moving load with a random amplitude is formulated in terms of the double forward Fourier transform of the non-stationary autocorrelation function. The solution procedure is illustrated with an example where the non-stationary autocorrelation function and the time-dependent standard deviation of the freefield response are computed for a moving harmonic load with a random phase shift. The results are compared with the response in the deterministic case.

[1]  H. Grundmann,et al.  The response of a layered half-space to traffic loads moving along its surface , 1999 .

[2]  Hem Hunt,et al.  Stochastic modelling of traffic-induced ground vibration , 1991 .

[3]  R. G. Payton.  An application of the dynamic Betti-Rayleigh reciprocal theorem to moving-point loads in elastic media , 1964 .

[4]  Geert Lombaert,et al.  Measurements and Numerical Prediction of High Speed Train Vibrations , 2004 .

[5]  Geert Lombaert,et al.  The experimental validation of a numerical model for the prediction of the vibrations in the free field produced by road traffic , 2003 .

[6]  Geert Lombaert,et al.  High speed train induced vibrations: in situ measurements and numerical modelling , 2003 .

[7]  Christian Madshus,et al.  HIGH-SPEED RAILWAY LINES ON SOFT GROUND: DYNAMIC BEHAVIOUR AT CRITICAL TRAIN SPEED , 2000 .

[8]  E. Kausel,et al.  Stiffness matrices for layered soils , 1981 .

[9]  Geert Lombaert,et al.  Numerical Modelling of Traffic Induced Vibrations , 2001 .

[10]  G. Lombaert.  Development and experimental validation of a numerical model for the free field vibrations induced by road traffic , 2001 .

[11]  Betsy S. Greenberg,et al.  DYNAMIC RESPONSE OF LINEAR SYSTEMS TO MOVING STOCHASTIC SOURCES , 2000 .

[12]  G. Roeck,et al.  Wave propagation in layered dry, saturated and unsaturated poroelastic media , 1998 .

[13]  J. E. Luco,et al.  Response of a layered viscoelastic half-space to a moving point load , 1994 .

[14]  Geert Lombaert,et al.  Numerical modelling of free field traffic-induced vibrations , 2000 .

[15]  R. J. Apsel,et al.  On the Green's functions for a layered half-space. Part II , 1983 .

[16]  Hong Hao,et al.  ANALYTICAL MODELING OF TRAFFIC-INDUCED GROUND VIBRATIONS , 1998 .

[17]  G. Degrande,et al.  Application of a Direct Stiffness Method to Wave Propagation in Multiphase Poroelastic Media , 1997 .

[18]  G. Lombaert,et al.  Experimental validation of a numerical prediction model for free field traffic induced vibrations by in situ experiments , 2001 .

[19]  J. D. Robson,et al.  The description of road surface roughness , 1973 .

[20]  Geert Lombaert,et al.  Validation of a numerical model for railway induced vibrations , 2003 .

[21]  G. Lombaert,et al.  An efficient formulation of Krylov's prediction model for train induced vibrations based on the dynamic reciprocity theorem. , 2000, The Journal of the Acoustical Society of America.

[22]  M.S.A. Hardy.  The generation of waves in infinite structures by moving harmonic loads , 1995 .

[23]  Gerhard Müller,et al.  Dynamische Bodenbeanspruchungen infolge bewegter Lasten , 1991 .

[24]  E. Wigner.  On the quantum correction for thermodynamic equilibrium , 1932 .

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

[26]  F E Branco.  International Symposium on the Environmental Impact of Road Pavement Unevenness , 1999 .