Finite-element transient calculation of a bell struck by a clapper

Abstract

A finite-element calculation of a bell struck by the bell clapper was performed as a transient contact problem. The geometry of the bell was taken from a real bell which was carved especially in behalf of this research. The eigenmodes and eigenfrequencies of the bell were calculated in advance, being in good agreement with the measured frequencies. The clapper/bell contact time and impulse shape show the expected behavior. The impulse shape is a Gaussian impulse with a tendency of a sharper attack slope and a softer decay slope. The periodical shape of the spectrum of this impulse caused by its finite width with zero values for some frequencies is shown. Nevertheless, this spectrum also drives the frequencies of the bell within the low-amplitude region of the driving impulse with expected and measured strength. The reason for this mode energy transfer is discussed. Furthermore, the sound of the bell is calculated as radiation from its surface and analyzed with signal-processing tools like wavelet transforms or autoregressive models.