Dynamic forces produced by swinging bells

The swinging of bells on belfries is a classical problem in structural dynamics and has been addressed in the Central European specialized bibliography. To carry out our study, the different modalities of swinging bells have been classified in “systems” according to their most relevant characteristics in three groups: Central European, English and Spanish systems. Each group presents some singular characteristics of frequency and oscillation, unbalance and/or turning rate, which give rise to different forces variable in time on their supporting structures. We have analyzed the three systems and, compared the maximum values of the horizontal and vertical forces that appear on the structure as well as its main harmonics. Besides the parameters analyzed, the complete dynamic study of the structure, and therefore the evaluation of its dynamic amplification factor (D.A.F.), requires the knowledge of its dynamic characteristics: main frequencies and damping ratio.