3D shape optimization of loudspeaker cabinets for uniform directivity

This paper presents a method to perform gradient-based shape optimization to minimize the root mean square deviation of the exterior acoustic sound pressure level distribution in front of an initially spherically shaped loudspeaker. The work includes several examples of how different multi-frequency optimization strategies can affect the final optimized design performance. This includes testing, averaging, and weighting of multi-frequency cost functions or using a minimax formulation. The shape optimization technique is based on an acoustic Boundary Element Method coupled to a Lumped Parameter loudspeaker model. To control and alter the deformation of the loudspeaker cabinet the optimization method adapts a spherical free-form deformation approach based on Bernstein polynomials. For the particular optimization problems presented, it is shown that improvements in the root mean square deviation of the sound pressure level in front of the loudspeaker can be achieved between 1 and 5 kHz. In the best-case scenario, less than a 1 dB sound pressure level (SPL) variation is observed between on-axis and a 70° off-axis response in the range 2 to 5 kHz. The widest frequency bandwidth and smoothest response of the root mean square deviation is found by utilizing the minimax formulation.