Archives of Acoustics, 34, 4, pp. 415-427, 2009

Numerical Simulation for the Bell Directivity Patterns Determination

Andrzej GOŁAŚ
AGH University of Science and Technology, Department of Mechanics and Vibroacoustics

Roman FILIPEK
AGH University of Science and Technology, Department of Mechanics and Vibroacoustics

The analysis of various sound sources is performed on the
basis of their directivity patterns. The literature does not contain any
information about directivity patterns of bells that are instruments broadly
applied to sacral purposes or to create a certain sound space from the aesthetic
point of view. The paper presents the methodology of determining the bell
directivity patterns by an example of the Russian bell. This example was applied
because exact values of geometrical parameters and measuring data of the bell
were available. The model was created by means of FEA (finite element analysis).
It included a coupling between the bell and its surrounding acoustic medium.
During the modal analysis, the first three natural frequencies of the bell were
calculated, and then, using the harmonic analysis, the directivity patterns were
determined for the frequencies. Afterwards, the transient response of the system
in selected measuring points was determined. The obtained results are important
for bell-founders and architects because thanks to the knowledge of directivity
patterns, the constructions supporting the bells can be designed in a better way
and the sound propagation can be determined more precisely. The presented method
of auralisation of the bell sound makes the cooperation between the designer and
the receiver fairly convenient.
Keywords: FEA; directivity patterns; musical instruments; idiophones; bell
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