A substructure approach tailored to the dynamic analysis of multi-span continuous beams under moving loads

The paper deals with the dynamic analysis of multiply supported continuous beams subjected to moving loads, which in turn can be modelled either as moving forces or moving masses. A dedicated variant of the component mode synthesis (CMS) method is proposed in which the classical primary–secondary substructure approach (SA) is tailored to cope with slender (i.e. Euler–Bernoulli) continuous beams with arbitrary geometry. To do this, the whole structure is ideally decomposed in primary and secondary spans with convenient restraints, whose exact eigenfunctions are used as assumed local modes; the representation of the internal forces is improved with the help of two additional assumed modes for each primary span, while primary–secondary influence functions allow satisfying the kinematical compatibility between adjacent spans; the continuous beam is then re-assembled, and the Lagrange's equations of motion are derived in a compact block-matrix setting for both moving force and moving mass model. Numerical examples demonstrate accuracy and efficiency of the proposed procedure. An application with a platoon of high-speed moving masses confirms that the inertial effects neglected in the moving force model may have a significant impact in the structural response.