Structural Analysis and Optimization of Bells Using Finite Elements
M. �zak�a, M.T. G� � · Journal of New Music Research · 2004
This paper deals with the structural analysis and shape optimization of bells. Using modal analysis it is possible to reconstruct the dynamic behavior of the bell by superposition of the excited eigenmodes. An examination of the nodal participation reveals that only a few of these modes are importance to the perceived sound the bell makes. From such consideration, tuning of bells is usually carried out by ensuring that the ratios of the first seven main frequencies (or partials) are in the correct proportions. Frequencies are determined using linear, quadratic and cubic, variable thickness, C (0) continuity, Mindlin-Reissner axisymmetric finite elements. The objective of shape optimization is to ensure that the ratios of the first seven main frequencies of bells are in the correct proportions. Several examples are included to illustrate the application of the analysis and optimization algorithm to the bells.