Bridging model and experiment in the design and validation of a sub-wavelength acoustic metamaterial

Abstract

Discrepancies between predicted and measured results often stem from fabrication errors in additive manufacturing, inaccurate assumptions in finite element analysis such as idealized sound-hard boundaries or imperfect analytical models. This paper highlights and partially tackles these issues while proposing a research direction to decouple process physics and designer expertise from the design process. A hybrid acoustic absorber is proposed, numerically simulated across different geometric configurations, additively manufactured for each case, and experimentally tested in an impedance tube. Despite good numerical and experimental agreement, high-cost numerical approaches are impractical for industrial design. To this end, a simplified numerical model (SNM) is developed by approximating the curvature of the embedded spiral with a straight tube. To minimize discrepancies, the analytical expression for the straight length is corrected with a simple formula, and the equivalent cavity is designed to account for the embedded spiral rather than utilizing the exact volume of the original cavity. The SNM agrees well with full-wave simulations while significantly reducing computational costs. In addition, to facilitate parametric studies and data-driven applications, an analytical model is presented and validated. The suitability of the various approaches for industrial design is evaluated. Challenges exist that are difficult to resolve with traditional modeling, especially for systems with intricate behavior, potentially limiting practical deployment. Our results underscore the need for improved methodology that is robust to imperfections, pushing acoustic metamaterial design beyond theoretical and numerical limitations.