"Modelling solutions for the linear dynamics of coupled TMD-bridge systems"

The paper deals with the continuous model of a planar beam, coupled with an auxiliary spring-mass damped oscillator, simulating the linear dynamics of a single-span footbridge equipped with a TMD. The model describes the shear discontinuity at the beam-oscillator connection. In virtue of a perturbation-based solution of the modal problem for the undamped system, local sensitivity analyses of the modal properties in the parameter space are carried out. In the resonant regions, in which the auxiliary oscillator is tuned to one of the beam frequencies, a marked phenomenon of frequency veering is described, while the global (beam) and the local (oscillator) resonant modes undergo a hybridization process. After a suited model reduction on the base of a pair of resonant hybrid modes, the exact and asymptotically approximate solutions of the complex modal analysis for the damped system are compared with their counterparts, as achievable according to a standard modelling approach, in which the oscillator is coupled to a one-degree-of-freedom model of the uncontrolled beam. The differences in the free and forced dynamic responses of the structure and the TMD, based on the different modelling solutions, are discussed.