Shape optimization of acoustic horns using few design variables

Abstract

The main steps for design of the optimal geometry of acoustic horns employing numerical methods are: the definition of the domain and the restrictions and control of the boundary, the definition of the objective function and the frequency range of interest, the evaluation of the objective function value, and the selection of a robust optimization technique to calculate the optimal value. During the optimization process, the profile is changing continuously until obtaining the optimal horn profile. The main focus of this work was to obtain optimal geometries with the use of few design variables. Two different methods to control the horn profile during the optimization process are used: approximation of the contour of the horn with Hermite polynomials and sinusoidal functions. The numerical results show the efficiency of these methods and it was also found (at least from the engineering point of view) that the solution is not unique to the geometry of the horn to single-frequency. The results for the optimization for more than one frequency are also shown.