Theory and inverse design of microperforated panels comprising arbitrary axial pore profiles for broadband low-frequency sound absorption

Toward identifying efficient sound absorbers, we have formulated and analyzed the micro-perforated panels (MPPs) comprising cylindrical pores of arbitrary axial profiles for out-of-plane wave propagation. First, the forward problem was solved wherein an exact analytical expression for the absorption coefficient alpha was developed for these MPPs. The dependence of alpha was analyzed for various profiles comprising convex and concave-shaped sections including divergent and convergent linear and sinusoidal profiles, conic sections, Kilroy, and chirp shapes. The MPPs with pores having a diverging shape at the entrance were found to have higher sound absorption. The non-symmetric fluctuations in the profile led to fluctuations in the spectrum of alpha. Aiming to address the long-standing challenge of low-frequency sound absorption, we solved the inverse problem to identify the axial profile of the cylindrical pore for maximum sound absorption for frequencies up to 2500 Hz. Given the advances in additive manufacturing, the results of this comprehensive work help in designing MPPs comprising complex-shaped pores suitable for a particular spectral regime.