Fusion of FEA and SEA for mid-frequency acoustics in a variable-section duct: Impedance-based coupling and experimental validation

Abstract

This work presents a fusion of finite element analysis (FEA) and statistical energy analysis (SEA) for calculating the mid-frequency response in a stepped acoustic duct comprising two chambers, Chamber 1 (0.644 × 0.045 × 0.045 m³) coupled to Chamber 2 (0.17 × 0.02 × 0.02 m³), arranged coaxially and driven by a loudspeaker at the outer end of Chamber 1. The system was tested in a fully anechoic room over 178 to 11220 Hz. Based on modal-number classification, Chamber 1 acted as a mixed 1D/3D subsystem over 1415 to 8913 Hz, and so was modeled statistically, whereas Chamber 2 remained 1D and was treated deterministically. The subsystems were coupled by an interface with impedance dynamically condensed to a single-degree-of-freedom. Absorption coefficients measured in an impedance tube were used to derive internal loss factors. Source characterization combined a multi-microphone approach for frequencies below the first cutoff at 3811 Hz and a plane-wave approximation for higher frequencies. The SEA solution for Chamber 1 yielded interface pressure and volume velocity, while pre-computed transfer functions predicted pressures at probe positions in Chamber 2. Experiments showed maximum errors of 2.88 dB in Chamber 1 and 3.02 dB in Chamber 2. The proposed method required 1009 s of computation, and is thus about 20 ×  faster than full-system FEA, which required 20061 s.