Acoustic horns optimization using finite elements and genetic algorithm

Abstract In this work the optimization of shape (geometry) of acoustic horns is analyzed. The finite element method is employed for calculating the sound pressure and optimization methods of zero order (Golden Line Search Method and Genetic Algorithm, GA) are used to obtain the optimal geometry. The shape of the horn is approximated locally using polynomials with C1 continuity with the objective to get a few design variables, to obtain smooth contours at each iteration and to eliminate the regularization of the common mesh in this type of optimization. It was also studied the influence of the size of the domain (environment) in the optimized geometry of the horn. The numerical results show the efficiency of this approach 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.

[1]  René Causse,et al.  Input impedance of brass musical instruments—Comparison between experiment and numerical models , 1984 .

[2]  Tonni F. Johansen,et al.  On the Directivity of Horn Loudspeakers , 1994 .

[3]  F. Ihlenburg.  Finite Element Analysis of Acoustic Scattering , 1998 .

[4]  Renato Barbieri,et al.  Finite element acoustic simulation based shape optimization of a muffler , 2006 .

[5]  Eddie Wadbro,et al.  An efficient loudspeaker horn designed by numerical optimization : An experimental study , 2010 .

[6]  Martin Berggren,et al.  Optimization of an acoustic horn with respect to efficiency and directivity , 2008 .

[7]  Vincent Pagneux,et al.  Wave Propagation In Acoustic Horns ThroughModal Decomposition , 1970 .

[8]  Renato Barbieri,et al.  Application of the Galerkin-FEM and the improved four-pole parameter method to predict acoustic performance of expansion chambers , 2004 .

[9]  Ivo Babuška,et al.  Reliability of infinite element methods for the numerical computation of waves , 1997 .

[10]  Renato Barbieri,et al.  The study of reactive silencers by shape and parametric optimization techniques , 2011 .

[11]  J. Z. Zhu,et al.  The finite element method , 1977 .

[12]  Martin Berggren,et al.  Shape optimization of an acoustic horn , 2003 .

[13]  A. Belegundu,et al.  Optimization Concepts and Applications in Engineering , 2011 .

[14]  Rolphe F. Fehlmann.  Computer simulations and application of numerical techniques for acoustic waves in curved Swiss horn , 1995 .