Advancements in Acoustic Topology Optimization

R. Christensen1
1Acculution ApS
Published in 2023

The design of products in the audio industry is to a large extent done via a combination of prior knowledge and trial-and-error. Such an approach will sometimes be seen described as an ‘optimization’ of said products, but we will here focus on the formal mathematical approach of optimization, specifically topology optimization with the underlying physics being acoustics. Topology optimization is still a relatively new technique with most of the defining work done within the last 50 years, with the focus being on structural mechanics applications. Acoustic topology optimization has had even fewer years to mature, and has for now remained mainly an academic exercise, whereas structural topology optimization has begun to creep into the industry.

In recent years, COMSOL has evolved its Optimization Module to a point where it is now possible to apply the academical learnings in the industry. In 2022, Acculution designed a phase plug for an acoustic waveguide for a (client’s) loudspeaker application purely via acoustic topology optimization, and this is seemingly the first in the world. When using the technique in the industry, the approaches described in the academic literature will typically not suffice, and we will touch upon some of the issues associated with industrial cases.

It will be demonstrated how acoustic topology optimization can result in designs that trial-and-error approaches could never achieve, as the solution space is too vast. The designs that emerge are required to meet targets across both a wide range of frequencies as well as across spatial angles, such as for controlling acoustical radiation patterns and directivity. In Figure 1 a design is shown that put in front of a tweeter can steer the radiation such that the initial on-axis response now is found at 20 degrees vertically off-axis. Such a design could be needed in car audio, where the drivers cannot be pointed towards the driver, and perhaps are situated inside some panels. Here, the acoustic cavity existing into the car cabin can be terminated by a topology optimized phase plug that guides the sound in the desired direction. This can also be relevant for home cinema installations, and in general for beam forming.

In some industrial cases, the physics setup related to the topology optimization may not have the desired symmetry axes that are sought in the final optimized design, so it is also demonstrated how auxiliary design constraints, such as extra mirror planes or repeating, possibly scaled, patterns can be implemented in the optimization setup without them being explicitly included in the physics setup. This is illustrated in Figure 2, where a mirror plane, which is not present in the acoustics setup, has been forced at the output of a topology optimized waveguide. With the technology having matured significantly in recent years, we expect to see other companies design parts of their products directly via acoustic topology optimization in the coming years, and the technique itself will likely continue to evolve more to for example meet certain manufacturing requirements.