Abstract
The dynamic responses of the railway and the carriage due to action of the multi-roller carriage were determined by means of the finite element method. Based on the dynamic equilibrium of a carriage and its suspension systems, the property matrices for the carriage were derived. The assembly of the last property matrices and those for the railway together with the elastic foundation yields the “time-dependent” overall property matrices and the equations of motions for the entire vibrating system, where the external loads on the railway are composed of the gravity forces due to axle rollers and carriage. By using the direct integration method, the equations of motions were solved to give the dynamic responses of the railway and the carriage. Since the effects of inertial forces due to the moving loads (carriage together with the axle rollers) and the effects of springs and dampers for the suspension systems are all considered and the total number of the axle rollers ranges from 2 to 4, the formulation of this paper may be the closest one in agreement with the practical situations among the existing literature. Therefore, the presented theory should be significant for the design of railway tracks.
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