Path-Following Bifurcation Analysis of Church Bell Dynamics

Abstract

In this paper, we perform a path-following bifurcation analysis of church bell to gain an insight into the governing dynamics of the yoke–bell–clapper system. We use an experimentally validated hybrid dynamical model based on the detailed measurements of a real church bell. Numerical analysis is performed both by a direct numerical integration and a path-following methods using a new numerical toolbox ABESPOL (Chong, 2016, “Numerical Modeling and Stability Analysis of Non-Smooth Dynamical Systems Via ABESPOL,” Ph.D. thesis, University of Aberdeen, Aberdeen, UK) based on COCO (Dankowicz and Schilder, Recipes for Continuation (Computational Science and Engineering), Society for Industrial and Applied Mathematics, Philadelphia, PA). We constructed one-parameter diagrams that allow to characterize the most common dynamical states and to investigate the mechanisms of their dynamic stability. A novel method allowing to locate the regions in the parameters' space ensuring robustness of bells' effective performance is presented.