Physical Bounds on Underwater Sound Absorption by Coatings

The development of sound-absorbing coatings for underwater structures has attracted significant attention due to their critical role in stealth and noise mitigation. While much of the recent research has focused on novel materials and complex configurations, the present study adopts a fundamentally different approach by establishing theoretical bounds on acoustic absorption that are independent of specific designs. Assuming only linearity and viscous damping, we model coatings using discrete mechanical elements characterized by mass, stiffness, and damping parameters. These models incorporate practical design constraints on added mass and hydrostatic compression of the coating. To identify configurations that maximize average acoustic absorption over a frequency range, we employ a Particle Swarm Optimization Algorithm that performs a global search over the constrained parameter space. A method for constraining the search space, which can be extended to any optimization algorithm, is presented and illustrated by examples. Perhaps surprisingly, our findings reveal that complex topologies yield only marginal performance gains compared to simpler configurations. For the canonical mass-spring-damper model, we derive closed-form approximations for absorption in the low-, mid-, and high-frequency regimes. These results establish performance ceilings for each topology, providing a benchmark for evaluating and guiding future material and structural innovations in underwater acoustic coatings.