Acoustic Filter Synthesis

Abstract

Mathematical programming has been applied to the synthesis of acoustic filters, eliminating the need for intuitive parameter selection and analysis. Variational methods applied through conjugate gradient techniques of Hestenes and Stiefel have been developed for two types of synthesis problems. Attenuation relationships presented for various muffler configurations by Davis et al. in NACA Report 1192, are used as the criteria function for which the filter parameters are optimized; that is, the use of a computational algorithm provides the length and area ratio which minimizes the difference between a desired attenuation and the available attenuation. Alternatively, a synthesis approach has been developed which provides the optimum parameters for an n-section filter, treated as cascaded sections of distributed parameter elements, subject to size and through flow constraints. This is an n-section generalization of the aforementioned approach and provides optimum parameters which minimize the difference between a desired output spectrum such as Walsh-Healey criteria and an output spectrum obtained for a given input. Results obtained using the two methods for a single expansion chamber are presented and compared.