Evaluating the response statistics of an uncertain bridge–vehicle system

Abstract This paper addresses the statistical prediction of dynamic response of a bridge structure with inherent uncertainty under stochastic moving loads. The uncertainty in bridge structure, which is assumed with Gaussian properties, is modeled by the Spectral Stochastic Finite Element Method. The uncertain moving forces with Gaussian distribution are represented by the Karhunen–Loeve expansion. The Polynomial chaos expansion is adopted to represent the uncertain response such that the proposed algorithm is not limited to system with small uncertainty. The bridge is modeled as a simply supported Bernoulli–Euler beam and the bridge–vehicle interaction forces are modeled as Gaussian random processes related to the power spectral density of the surface roughness defined in the ISO standard. The mathematical model of the bridge–vehicle system is formulated and solved with the Newmark-β method. The response statistics of the bridge are compared with those from Monte Carlo simulation. Different levels of uncertainty in both the system parameters and the moving forces are studied to investigate the accuracy and robustness of the proposed method in the stochastic analysis of the bridge–vehicle interaction problem.

[1]  Mircea Grigoriu,et al.  On the accuracy of the polynomial chaos approximation for random variables and stationary stochastic processes. , 2003 .

[2]  T.-P. Chang,et al.  Vibration analysis of a beam with an internal hinge subjected to a random moving oscillator , 2006 .

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

[4]  R. Clough,et al.  Dynamics Of Structures , 1975 .

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

[6]  G. I. Schuëller,et al.  Developments in stochastic structural mechanics , 2006 .

[7]  Roger Ghanem,et al.  Ingredients for a general purpose stochastic finite elements implementation , 1999 .

[8]  S. S. Law,et al.  DYNAMIC BEHAVIOR OF ORTHOTROPIC RECTANGULAR PLATES UNDER MOVING LOADS , 2003 .

[9]  Ton-Lo Wang,et al.  DYNAMIC RESPONSE OF MULTIGIRDER BRIDGES , 1992 .

[10]  Christian A. Schenk,et al.  Uncertainty assessment of large finite element systems , 2005 .

[11]  Giuseppe Muscolino,et al.  Dynamics analysis of distributed parameter system subjected to a moving oscillator with random mass, velocity and acceleration , 2002 .

[12]  R. Ghanem,et al.  A stochastic projection method for fluid flow. I: basic formulation , 2001 .

[13]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[14]  Rong Tyai Wang,et al.  Vibration of Multi-Span Timoshenko Beams to a Moving Force , 1997 .

[15]  Xinqun Zhu,et al.  Vehicle axle loads identification using finite element method , 2004 .

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

[17]  Roger Ghanem,et al.  Stochastic inversion in acoustic scattering , 2006 .

[18]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[19]  Aleš Florian,et al.  An efficient sampling scheme: Updated Latin Hypercube Sampling , 1992 .

[20]  David Cebon,et al.  Dynamic Response of Highway Bridges to Heavy Vehicle Loads: Theory and Experimental Validation , 1994 .

[21]  S. S. Law,et al.  Bridge dynamic responses due to road surface roughness and braking of vehicle , 2005 .

[22]  Chao Yang,et al.  Solving Large-scale Eigenvalue Problems in SciDAC Applications , 2005 .

[23]  Luigi Garibaldi,et al.  Dynamics of multi-span continuous straight bridges subject to multi-degrees of freedom moving vehicle excitation , 1999 .

[24]  Nicholas Zabaras,et al.  A stochastic variational multiscale method for diffusion in heterogeneous random media , 2006, J. Comput. Phys..

[25]  Nicholas Zabaras,et al.  A non-intrusive stochastic Galerkin approach for modeling uncertainty propagation in deformation processes , 2007 .

[26]  S. S. Law,et al.  Dynamic behavior of damaged concrete bridge structures under moving vehicular loads , 2004 .

[27]  N. Wiener.  The Homogeneous Chaos , 1938 .

[28]  T. P. Chang,et al.  Vibration analysis of a uniform beam traversed by a moving vehicle with random mass and random velocity , 2009 .

[29]  M. Kac,et al.  An Explicit Representation of a Stationary Gaussian Process , 1947 .

[30]  Ton-Lo Wang,et al.  Vibration of highway steel bridges with longitudinal grades , 1998 .

[31]  Gouri Dhatt,et al.  An Efficient Algorithm for Dynamic Analysis of Bridges Under Moving Vehicles Using a Coupled Modal and Physical Components Approach , 1998 .

[32]  T. Kocatürk,et al.  Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load , 2006 .

[33]  Roger Ghanem,et al.  Efficient solution of stochastic systems: Application to the embankment dam problem , 2007 .

[34]  Sq Q. Wu,et al.  Dynamic analysis of bridge–vehicle system with uncertainties based on the finite element model , 2010 .

[35]  H. Najm,et al.  A stochastic projection method for fluid flow II.: random process , 2002 .

[36]  M. Shinozuka,et al.  Simulation of Stochastic Processes by Spectral Representation , 1991 .