Achieving optimal attenuation in acoustic waveguides with 3D printed Helmholtz resonators

A double root, commonly referred to as an exceptional point (EP), for modal frequencies in a 2D or 3D waveguide can exhibit optimal attenuation rates over a relatively broad frequency range. The key to the phenomenon is that the wall impedance is such that modes coalesce at a complex-valued frequency. In this talk we consider a novel approach to feasibly achieve the aforementioned wall impedance with the use of simple resonators, which can be shown to exhibit mode coalescence at distinct frequencies when treated as a unit cell component of a larger metasurface. Numerical results of several unit cell designs are given to test the boundaries on the following constraints: realizable resonator dimensions, scale separation, and target attenuation goals. To validate the analytical work, experimental setups consisting of additively manufactured Helmholtz resonators incorporated onto a custom-made impedance tube are tested. The dependence of printed resonator quality on theoretical inertial, loss, and stiffness values are discussed in tandem with printing repeatability. Simulated finite element model results will be used as comparative backdrops with the numerical and experimental results. Work supported by NSF.