A fast mode superposition algorithm and its application to the analysis of bridges under moving loads

Modal superposition (MS) techniques are widely used in linear dynamic analyses but the study of large structures subject to actions such as long vehicle convoys is not currently feasible. This work presents an algorithm called MS5 embedded in the Python library MDyn that combines an efficient indexing strategy to deactivate specific structural nodes and movements with a novel modal truncation based on a new dynamic participation factor and the vectorisation of the MS algorithm. The MS5 is compared with the conventional MS method, the analytical solution and the commercial finite element software ABAQUS in the dynamic analysis of a short-span beam bridge and of a large cable-stayed bridge under different load scenarios. The results obtained with MS5 are almost identical to other methods, but it is on average 9 times faster than the standard MS method. The proposed algorithm is applied to the study of critical traffic actions in both structures, observing important dynamic amplification effects for certain convoy arrangements that are able to trigger resonant responses in the deck. MS5 is also applicable to other line-like structures such as towers, masts, etc.