Impact adding bifurcation in an autonomous hybrid dynamical model of church bell

P. Brzeski, A. S. E. Chong, M. Wiercigroch, P. Perlikowski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


In this paper we present the bifurcation analysis of the yoke-bell-clapper system which corresponds to the biggest bell “Serce Lodzi” mounted in the Cathedral Basilica of St Stanislaus Kostka, Lodz, Poland. The mathematical model of the system considered in this work has been derived and verified based on measurements of dynamics of the real bell. We perform numerical analysis both by direct numerical integration and path-following method using toolbox ABESPOL (Chong, 2016). By introducing the active yoke the position of the bell-clapper system with respect to the yoke axis of rotation can be easily changed and it can be used to probe the system dynamics. We found a wide variety of periodic and non-periodic solutions, and examined the ranges of coexistence of solutions and transitions between them via different types of bifurcations. Finally, a new type of bifurcation induced by a grazing event - an “impact adding bifurcation” has been proposed. When it occurs, the number of impacts between the bell and the clapper is increasing while the period of the system's motion stays the same.

Original languageEnglish
Pages (from-to)716-724
Number of pages9
JournalMechanical Systems and Signal Processing
Early online date1 Dec 2017
Publication statusPublished - 1 May 2018

Bibliographical note

Acknowledgement: This study was supported by Lodz University of Technology (K113/9117DS). PB is supported by the Foundation for Polish Science (FNP).


  • Bells
  • Bifurcation analysis
  • Hybrid system
  • Impact adding bifurcation
  • Impacts
  • Nonlinear dynamics


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