Elucidating Structure-Property relationships for optimization of plate lattice sound absorbers

Abstract

To be compatible with mainstream additive manufacturing techniques, plate lattices must be designed with embedded pores to eliminate closed cells and facilitate material removal. Interestingly, these pores also transform the plate lattices into effective acoustic absorbers, with structures resembling Helmholtz resonators. In this work, the sound absorption performance of plate lattices inspired by crystal structures was investigated, with small perforations at nodes introduced as a design feature to facilitate feedstock material removal and allow acoustic energy to penetrate the structure. Calibrated through numerous additively manufactured samples, a high-fidelity mathematical model, grounded in Helmholtz resonance principles and the Transfer Matrix Method, was developed to accurately predict the acoustic properties of plate lattices across a broad range of frequencies from 450 to 6300 Hz. The model not only effectively predicts sound absorption coefficient curves based on geometric parameters but also provides valuable insights into how these parameters influence acoustic performance. It is found that smaller cell sizes, higher relative densities, and reduced perforation sizes generally result in higher mean sound absorption coefficients. The frequency bands of peak absorption regions are then strongly affected by the perforation size relative to the cell size. Furthermore, an optimization framework leveraging the model generated heterogeneous plate lattice designs with superior broadband sound absorption at targeted frequency ranges. This work introduces a robust mathematical approach for predicting and optimizing the acoustic properties of perforated plate lattices while uncovering key structural-property relationships that drive their performance.