Modal decomposition method for acoustic impedance testing in square ducts

Accurate duct acoustic propagation models are required to predict and reduce aircraft engine noise. These models ultimately rely on measurements of the acoustic impedance to characterize candidate engine nacelle liners. This research effort increases the frequency range of normal-incidence acoustic impedance testing in square ducts by extending the standard two-microphone method (TMM), which is limited to plane wave propagation, to include higher-order modes. The modal decomposition method (MDM) presented includes four normal modes in the model of the sound field, thus increasing the bandwidth from 6.7 to 13.5 kHz for a 25.4 mm square waveguide. The MDM characterizes the test specimen for normal- and oblique-incident acoustic impedance and mode scattering coefficients. The MDM is first formulated and then applied to the measurement of the reflection coefficient matrix for a ceramic tubular specimen. The experimental results are consistent with results from the TMM for the same specimen to within the 95% confidence intervals for the TMM. The MDM results show a series of resonances for the ceramic tubular material exhibiting a monotonic decrease in the resonant peaks of the acoustic resistance with increasing frequency, resembling a rigidly-terminated viscous tube, and also evidence of mode scattering is visible at the higher frequencies.