Reverse engineering techniques for investigating the vibro-acoustics of historical bells

In this paper, we present an effective methodology for assessing the vibrational properties of real-life bells, using reverse engineering techniques. When struck by a clapper, bells vibrate in rather complicated ways, which result in complex sounds. Typically, to obtain pleasant sounds, bell founders tune the first five partials (vibration modes) according to specific frequency ratios, while also trying to control the amount of beats, which also affect the musical quality. In practice, many musically important aspects are strongly related to fine details of the bell geometry. In this work, we use scanning imaging technology to obtain precise 3D geometry bell data, and then assess the bell tuning features by combining the acquired 3D geometrical data with Finite Element modal computations. Our numerical results are compared with experimentally identified bell modes, attesting the feasibility and effectiveness of the proposed approach. This analysis strategy is particularly suited in the context of cultural heritage preservation, by providing new and comprehensive ways to characterize and describe historical bells. Moreover, it can also shed light when addressing bell casting and tuning techniques throughout times.