A substructure approach in the dynamic analysis of continuous beams under moving oscillators

When dealing with the vehicle-induced vibration of continuous bridges, the dynamic excitation is usually modelled through moving forces or masses, in so neglecting the bridge-vehicle interaction. In this paper, intended at studying the effects of this important phenomenon, a novel technique for the dynamic analysis of multi-span inhomogeneous beams carrying moving oscillators is presented and numerically validated. The proposed formulation is based on a special variant of the Component Mode Synthesis (CMS) method, herein used with the aim of decomposing the continuous beam in an ideal series of alternate primary and secondary spans of convenient boundary conditions. Once the compatibility between adjacent spans is re-established, a set of effective shape functions for the whole continuous beam are defined. Finally, the associated Lagrange’s equations of motion for the beam-oscillator system are derived and arranged in a compact state-space form, very efficient for practical implementations.