Tuning a wine glass via material tailoring - An application of a method for optimal acoustic design

This paper describes a method for optimally designing a structure to "best fit" a specified set of acoustic characteristics, e.g., sound spectrum or radiated power. The method links the disciplines of structural dynamics, acoustics and optimization into a unified methodology. The design variables include, for example, the addition of masses or multiply-tuned resonators to the structure as well as distributions of stiffeners or constrained damping layers. In all cases, the design variables are introduced as external forces (via their impedances) in the equation for the structure that is given 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 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. To illustrate the design method, a wine glass is tuned optimally to move the first four eigenvalues into harmonic relationships. The design variables are small masses that are added to the upper surface of the wine glass. Comparison of the wine glass's radiated sound power with and without the optimal masses indicates an excellent agreement between the specified and measured spectra.