Swinging-bell resonances and their cancellation identified by dynamical testing in a modern bell tower

The occurrence of the resonance phenomenon causes high amplitude dynamic vibrations in slender structures. This paper presents an archetypal example. including analysis and mitigating intervention, based on the real case study of a bell tower. Resonances between the multi-harmonic swinging motion of five oscillating bells and the first natural frequency of the supporting system. namely a modern tower realized in reinforced concrete, are clearly demonstrated. Using ambient vibration acceleration measurements, the modal parameters of the tower are identified consistently by two different output-only procedures: the first, based on the Complex Mode Identification Function, exploits a frequency representation of the response; the second, based on the Stochastic Subspace Identification Method, works in the time domain. The frequency characteristics of the bell-swinging action are determined through spectral analyses of the structure forced response signals, measured during the swinging motion of each bell separately. The closeness of the tower's first natural frequency with the third harmonic of the dynamic horizontal force transmitted to the structure by the two heaviest swinging bells is recognized as the source of large oscillations. A finite element model is developed and manually updated to accurately reproduce the tower's spectral properties and to design a structural intervention for the vibration mitigation. The resonance cancellation obtained through the introduction of a stiffening strut is demonstrated to limit the bell-induced oscillations effectively, as verified by a post-intervention dynamic test campaign