Tuning a Replica of the Liberty Bell via Material Tailoring: An Application of a Method for Optimal Acoustic Design

Abstract

In this paper we describe a method for optimally tuning a bell to ‘best fit’ a specified sound spectrum. The method links the disciplines of structural dynamics, acoustics and optimization into a unified methodology. The design variables center on the addition of masses (size, number and location). The design variables are treated as external forces (via their impedances) in the equation that describes the bell dynamics as a series expansion of eigen functions. This step eliminates the need for solution of large matrix eigenvalue problems. An acoustic program POWER is used to assess the bell’s radiated sound power as a function of the design variables. Various search engines are used within the computer program MATLAB® to determine which design variables give the ‘best fit’ to the acoustic specifications.