Spectral method in realistic modelling of bridges under moving vehicles

Abstract

This paper develops techniques for application of spectral method in dynamics of structures, particularly bridges under the moving loading. Spectral method is formulated in terms of matrix operators capable of discretizing and combining Kirchhoff–Love plates and Bernoulli beams. The boundary conditions have been imposed using Lagrange multipliers so combinations of Dirichlet and Neumann conditions could be dealt with. The proposed method allows a bridge to be represented as a 3D structure with realistic cross-section (ribs, box girders, etc.).Moving loading can be any realistic model of a vehicle such as standard European three-axle road vehicle with 9 dynamic degrees of freedom. Vehicle behaviour is described with an additional system of differential equations that has to be solved together with a partial differential equation of the bridge model. Two different formulations and the corresponding methods of solution are presented: (i) formulation suitable for direct solution and (ii) formulation suitable for semi-direct (staggered) solution.The proposed approach based upon the spectral matrix operators is sufficiently general to be suitable for dealing with strong form of any structure analysis problem. Example of dynamic analysis of a real bridge in Croatia illustrates the proposed method.