This article describes the design of the profile for a major-third bell using structural optimization strategies. First a sequential linear programming method was used to find a prototype of the bell. The necessary analyses were done using the finite element method. Next, a fast analysis model was derived by numerical experimental design techniques. This analysis model led to the final geometry of the major-third bell.


Cox, D. R. Planning of experiments. New York: John Wiley & Sons, 1958.
Dantzig, G. Linear programming and extensions. Princeton, NJ: Princeton Univ. Press, 1963.
Kirsch, U. Optimum structural design. New York: McGraw-Hill, 1981.
Lehr, A. Partial groups in the bell sound. Journal of the Acoustical Society of America, 1986, 72,2000-2011.
Zienkiewicz, O. C. The finite element method. London: McGraw-Hill Book Company (U.K.) Limited, 1977.
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