Acoustic Control Mechanism of Multilayer Composite Structure Based on Statistical Energy Analysis and Transfer Matrix Algorithm

Abstract

To overcome the limitations of traditional single-layer materials in broadband sound absorption and the inadequacy of existing simulation methods for complex composite structures, this study proposes a hybrid modeling framework that integrates Statistical Energy Analysis (SEA) and Transfer Matrix Method (TMM). A cross-scale theoretical model is established to map material micro-parameters (flow resistivity, porosity, tortuosity) to macroscopic SEA subsystem parameters, enabling precise low-frequency wave description via TMM and efficient mid-to-high frequency statistical energy characterization via SEA. Comparative simulations reveal a fundamental divergence between the two methods: at 16 Hz, pure TMM predicts a transmission loss (TL) of only 0.44 dB, whereas SEA predicts 48.62 dB – a discrepancy exceeding 48 dB – highlighting TMM's idealized infinite-layer assumptions versus SEA's system-level boundary considerations. Based on these findings, a frequency-domain weighted fusion model is developed, employing a Sigmoid weighting function calibrated by experimental data to achieve a smooth transition between the two methods across the full spectrum. The proposed SEA-TMM hybrid model reduces the root-mean-square error (RMSE) of TL prediction by 52 % compared to pure SEA and 93 % compared to pure TMM, providing a robust cross-scale theoretical tool for the high-performance design of complex multilayer acoustic materials.