Efficient multimodal-based shape optimization of acoustic horns with application to subwavelength perfect transmission

This paper presents an efficient multimodal-based shape optimization method for maximizing sound radiation from open-ended acoustic horns. The proposed method tightly integrates the improved multimodal admittance method with interpolation-based geometry parameterization to allow flexible design degrees of freedom, with computational cost for gradient evaluation nearly independent of the number of design variables. We demonstrate that our method outperforms an existing discrete-model-based approach in solving typical narrowband and wideband horn design problems, offering increased efficiency and flexibility. For the first time, we achieve novel resonator-like waveguide designs with subwavelength perfect transmission well below the cut-off frequency of classical horns by performing shape optimization. The optimal waveguides exhibit single to multiple transmission peaks or bandpass characteristics. We validate the designs numerically and experimentally and demonstrate that the perfect transmission is related to the excitation of the acoustic resonant mode. Our method has potential applications in the design of compact high-output subwoofers, anechoic duct terminations, and acoustic filters.