Modeling and Experimental Investigation of Two-Dimensional Higher-Order Mode Propagation through Acoustic Metamaterials

Abstract

Airplane noise has adverse effects on communities, and it is mitigated using technologies such as turbofan nacelle liners to attenuate engine noise. These liners can be classified and analyzed as acoustic metamaterials (AMM). Specifically, the traditional perforate-over-honeycomb liner configuration can be modeled as a periodic array of Helmholtz resonators. Historically, analytical models for these Helmholtz resonator arrays have been limited to 1D plane wave propagation, neglecting the complex effects of higher-order mode (HOM) propagation. This thesis addresses this gap by extending traditional AMM modeling techniques to 2D to accommodate HOM propagation. The transfer matrix method (TMM) is utilized in conjunction with Bloch wave theory to develop two distinct analytical frameworks. One model assumes decoupled modal propagation while the other incorporates mode coupling behavior. The results of these analytical formulations are validated and compared with experimental data obtained from a grazing incidence impedance tube modified to accommodate HOM generation and propagation. Analytical results demonstrate that peaks in transmission loss correspond directly to the locations of the predicted theoretical stop bands. While plane wave experimental testing successfully verifies the analytical predictions, multi-modal experimental results exhibit deviations due to inter-modal scattering and physical non-idealities. Overall, the modeling techniques established in this thesis provide a strong theoretical foundation for evaluating AMM performance without relying solely on extensive physical testing.