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

被引：22

作者：

Brzeski, P. ^{[1
]}

Chong, A. S. E. ^{[2
]}

Wiercigroch, M. ^{[3
]}

Perlikowski, P. ^{[1
]}

机构：

[1] Tech Univ Lodz, Div Dynam, Stefanowskiego 1-15, PL-90924 Lodz, Poland

[2] Escuela Super Politecn Litoral, Fac Ciencias Nat & Matemat, POB 09-01-5863, Guayaquil, Ecuador

[3] Univ Aberdeen, Kings Coll, Sch Engn, Ctr Appl Dynam Res, Aberdeen AB24 3UE, Scotland

来源：

MECHANICAL SYSTEMS AND SIGNAL PROCESSING | 2018年 / 104卷

关键词：

Bells; Nonlinear dynamics; Impacts; Hybrid system; Bifurcation analysis; Impact adding bifurcation; GRAZING BIFURCATIONS; OSCILLATORS; VERIFICATION; FORCES;

D O I：

10.1016/j.ymssp.2017.11.025

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

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. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：716 / 724

页数：9

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