| Abstract: | An iterative solution method is presented and illustrated to analyse the dynamic response of bridge–vehicle systems. The method consists in dividing the whole system into 2 subsystems at the interface of the bridge and vehicles; these 2 subsystems are solved separately; their compatibility at the interface is achieved by an iterative procedure with under-relaxation or with Aitken acceleration. The characteristics of this method are explained on a simplified system with 2 degrees of freedom (DOF). The numerical results for a simple example demonstrate the high performances of the proposed method: good convergence rate and high accuracy. Finally, the method is applied to a practical example: the linear dynamic response of the Yangtze-River Bridge at Wuhan under a moving train with 2 locomotives and 4 freight cars. The efficiency is attained because neither formation nor factorisation of the coefficient matrices for the equations of the system are needed at every time step in linear analysis. The Aitken acceleration technique is more efficient in systems with multi-degrees of freedom than the relaxation technique. The proposed method will be even more efficient in non-linear dynamic response because, in this case, the iterations are necessary whether the system is solved as a whole or not. |
