Dynamic behaviour of masonry church bell towers

Several masonry church bell towers situated in north-east England were forced to vibrate by tolling single bells. The fundamental natural frequencies, mode shapes and damping factors for the sway modes of the towers were deduced from the traces of the tower responses obtained using geophones and/or accelerometers. The natural frequencies in the north-south and east west directions and associated levels of damping are generally similar. The sway mode comprises components of rocking, shear and bending deformations all of which are generally significant. The shear component was found to be the most critical contribution to the response. Using a computer program PAFEC based on the finite element method of structural analysis selected towers were modelled as monolithic structures using beam or brick finite elements. The periodic forces due to bell ringing were computed by assuming that the bells behaved as compound pendulums. Then the tower responses were computed using a numerical technique to solve the differential equations governing their forced vibration. To allow for masonry joints and other uncertainties concerning the structural fixity of the towers, the Young's modulus and density of the sandstone used in their construction were adjusted to provide the best agreement between the computed and measured natural frequencies, mode shapes and dynamic responses of the towers. It was found that the overall adjustment factors varied from 0.07 to 0.37 for the Young's modulus and from 0.33 to 1.09 for the density.