TY - JOUR
T1 - Path-Following Bifurcation Analysis of Church Bell Dynamics
AU - Chong Escobar, Antonio Simon
AU - Brzeski, Piotr
AU - Wiercigroch, Marian
AU - Perlikowski, Przemyslaw
N1 - This work was supported by: P.B. acknowledges the grant from the National Science Center Poland (Decision No. DEC-2015/16/T/ST8/00516) and the support by the Foundation for Polish Science (FNP), the National Secretariat of Science, Technology and Innovation of Ecuador, and the Escuela Superior Politécnica del Litoral of Guayaquil, Ecuador.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85029180943&partnerID=8YFLogxK
U2 - 10.1115/1.4036114
DO - 10.1115/1.4036114
M3 - Article
AN - SCOPUS:85029180943
SN - 1555-1415
VL - 12
SP - 1
EP - 8
JO - Journal of Computational and Nonlinear Dynamics
JF - Journal of Computational and Nonlinear Dynamics
IS - 6
M1 - 061017
ER -