Vibration of bell towers excited by bell ringing - a new approach to analysis

摘要

Bell ringing is popular worldwide, especially in churches. In change ringing, especially popular in the UK, as many as twelve bells swing bodily through 360° and the mass of the heaviest bell is typically well in excess of 1000kg. Such bells are generally located some way up a bell tower and the horizontal forces generated by their swinging can cause substantial - and often damaging - levels of vibration at frequencies typically around 2Hz. Even small amplitudes of vibration, say 2mm, are known to create difficulties because of the precise timing required to ring changes to a given "method". In addition, a peal lasts roughly 3 hours 20 minutes and energy to vibrate the tower is energy extracted from the bell ringers' muscular effort leading more rapidly to exhaustion. This paper outlines a new method for analysing the motion of a tower during bell ringing. Traditionally it has been considered sufficient to keep odd harmonics of the fundamental period of the bell away from resonances of the tower and to avoid placing bells high up in towers with low-damped resonances in the vicinity of 1-2Hz. The new method is much more precise than this and it examines the forces of all bells as they progress through a given method. Based on some simple data measured from the tower it is possible to compute the amplitude of tower motion with some considerable accuracy. It is found that even harmonics excite tower motion significantly and that this is related to the size of the handstroke gap. It is also found that total peal time has a big influence on tower motion. The paper presents a case study on the vibration of the bell tower in Great St Mary, Cambridge, which has been home to bell ringing since 1724 - the second oldest ringing society at any church in the world with a continuous history of its ringing.