A Modified Bridge System method to characterize and decouple vehicle–bridge interaction

This paper examines the effect of traversing vehicles on the vibration of the supporting bridge. It shows that the effect of vehicle–bridge interaction (VBI) on the mechanical system of the bridge breaks down into three constituent mechanisms: (a) an additional damping, (b) an additional stiffness, and (c) a modified loading term. The study characterizes these three mechanisms with explicit analytical expressions in the case of a single-degree of freedom (SDOF) vehicle–SDOF bridge system. The analysis reveals that the impedance ratio—defined as the ratio of the vehicle’s damping to the bridge’s mechanical impedance—is a dominant coupling parameter of VBI, in addition to the (well-known) vehicle-to-bridge stiffness ratio. Subsequently, the study proposes an original approach, namely the Modified Bridge System (MBS) method, to decouple the VBI problem when the stiffness ratio is small. The MBS approach solves a modified bridge system, independent of the traversing vehicle. Numerical applications on simply supported railway bridges show that the MBS method outperforms other decoupling approaches, such as the moving load approximation. At the same time, compared to the solution of the coupled vehicle–bridge system, the proposed MBS method is equally accurate but computationally more efficient. The paper also outlines limitations of the proposed approach related to the single-mode representation of both vehicle and bridge.

[1]  Chul-Woo Kim,et al.  Experimental monitoring of bridge frequency evolution during the passage of vehicles with different suspension properties , 2019, Engineering Structures.

[2]  Yeong-Bin Yang,et al.  VEHICLE-BRIDGE INTERACTION ANALYSIS BY DYNAMIC CONDENSATION METHOD. DISCUSSION AND CLOSURE , 1995 .

[3]  Nicos Makris,et al.  Dimensional analysis of the earthquake‐induced pounding between adjacent structures , 2009 .

[4]  D. S. Kothari.  III. A note on Doppler effect and the hypothesis of radiation quanta , 1929 .

[5]  Rui Calçada,et al.  A direct method for analyzing the nonlinear vehicle–structure interaction , 2012 .

[6]  Eugene J. O'Brien,et al.  The non-stationarity of apparent bridge natural frequencies during vehicle crossing events , 2013 .

[7]  Yeong-Bin Yang,et al.  Vehicle–bridge interaction dynamics and potential applications , 2005 .

[8]  C. Teitelboim.  RADIATION REACTION AS A RETARDED SELF-INTERACTION. , 1971 .

[9]  Kai Liu,et al.  The effect of dynamic train–bridge interaction on the bridge response during a train passage , 2009 .

[10]  Daniel Cantero,et al.  Evolution of bridge frequencies and modes of vibration during truck passage , 2017 .

[11]  Jing Zeng,et al.  Estimation of the damping effects of suspension systems on railway vehicles using wedge tests , 2016 .

[12]  Yeong-Bin Yang,et al.  Resonance of high-speed trains moving over a series of simple or continuous beams with non-ballasted tracks , 2017 .

[13]  Hui Guo,et al.  Recent developments of high-speed railway bridges in China , 2017 .

[14]  Yeong-Bin Yang,et al.  FREQUENCY VARIATION IN VEHICLE–BRIDGE INTERACTION SYSTEMS , 2013 .

[15]  Yeong-Bin Yang,et al.  EXTRACTING BRIDGE FREQUENCIES FROM THE DYNAMIC RESPONSE OF A PASSING VEHICLE , 2002 .

[16]  M. D. Martínez-Rodrigo,et al.  Influence of the vehicle model on the prediction of the maximum bending response of simply-supported bridges under high-speed railway traffic , 2014 .

[17]  Anil K. Chopra,et al.  Dynamics of Structures: Theory and Applications to Earthquake Engineering , 1995 .

[18]  Charikleia D. Stoura,et al.  A localized lagrange multipliers approach for the problem of vehicle-bridge-interaction , 2018 .

[19]  Elias G. Dimitrakopoulos,et al.  A three-dimensional dynamic analysis scheme for the interaction between trains and curved railway bridges , 2015 .

[20]  Chul-Woo Kim,et al.  Effect of train dynamics on seismic response of steel monorail bridges under moderate ground motion , 2006 .

[21]  Nicos Makris,et al.  Dimensional Analysis of the Earthquake Response of a Pounding Oscillator , 2010 .

[22]  E. Buckingham.  On Physically Similar Systems; Illustrations of the Use of Dimensional Equations , 1914 .

[23]  Helmut J. Pradlwarter,et al.  Reliability assessment of railway bridges subjected to high-speed trains considering the effects of seasonal temperature changes , 2016 .

[24]  G. I. Barenblatt.  Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics , 1996 .

[25]  Nan Zhang,et al.  Dynamic Interaction of Train-Bridge Systems in High-Speed Railways , 2018 .

[26]  Yeong-Bin Yang,et al.  Vibration of simple beams due to trains moving at high speeds , 1997 .

[27]  Christoph Adam,et al.  A Stochastic View on the Effect of Random Rail Irregularities on Railway Bridge Vibrations , 2019, Structure and Infrastructure Engineering.

[28]  Xiaozhen Li,et al.  High-speed train–track–bridge dynamic interactions – Part I: theoretical model and numerical simulation , 2013 .

[29]  Charikleia D. Stoura,et al.  Additional damping effect on bridges because of vehicle-bridge interaction , 2020, Journal of Sound and Vibration.

[30]  Yeong-Bin Yang,et al.  Vehicle-bridge interaction dynamics: with applications to high-speed railways , 2004 .

[31]  Kuang-Han Chu,et al.  DYNAMIC INTERACTION OF RAILWAY TRAIN AND BRIDGES , 1980 .

[32]  Michael Oberguggenberger,et al.  On computational interdisciplinary modeling for reliability assessment of high‐speed train – bridge interaction , 2018, PAMM.

[33]  Nan Zhang,et al.  Consideration of nonlinear wheel–rail contact forces for dynamic vehicle–bridge interaction in high-speed railways , 2013 .

[34]  M. M. Stanišić.  On a new theory of the dynamic behavior of the structures carrying moving masses , 1985 .

[35]  M. D. Martínez-Rodrigo,et al.  An equivalent additional damping approach to assess vehicle-bridge interaction for train-induced vibration of short-span railway bridges , 2019, Engineering Structures.

[36]  Ton-Lo Wang,et al.  Railway Bridge/Vehicle Interaction Studies with New Vehicle Model , 1991 .

[37]  Yeong-Bin Yang,et al.  Vertical and pitching resonance of train cars moving over a series of simple beams , 2015 .

[38]  Yeong-Bin Yang,et al.  Dynamic Response of High Speed Vehicles and Sustaining Curved Bridges Under Conditions of Resonance , 2016 .

[39]  S. Timoshenko,et al.  X. On the transverse vibrations of bars of uniform cross-section , 1922 .

[40]  Ladislav Frýba,et al.  Dynamics of Railway Bridges , 1996 .

[41]  T. Tsao,et al.  On asymptotics of the solution of the moving oscillator problem , 2003 .

[42]  Stephen P. Timoshenko,et al.  Vibration problems in engineering , 1928 .

[43]  Guido De Roeck,et al.  Dynamic analysis of high speed railway bridge under articulated trains , 2003 .

[44]  E. Dimitrakopoulos,et al.  Vehicle–bridge interaction analysis modeling derailment during earthquakes , 2018 .

[45]  Christoph Adam,et al.  Modeling of dynamic train–bridge interaction in high-speed railways , 2015 .

[46]  Elias G. Dimitrakopoulos,et al.  Seismic response analysis of an interacting curved bridge–train system under frequent earthquakes , 2016 .

[47]  Patrick J. McGetrick,et al.  Experimental validation of a drive-by stiffness identification method for bridge monitoring , 2015 .

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

[49]  Chul-Woo Kim,et al.  Variability in bridge frequency induced by a parked vehicle , 2014 .

[50]  Raid Karoumi,et al.  Statistical screening of modelling alternatives in train–bridge interaction systems , 2014 .