2025/06/18 by Humbert, Sylvain C.
Engineering · #500 Naturwissenschaften und Mathematik::530 Physik::530 Physik #Acoustic Wave Phenomena Research #Aerodynamics and Acoustics in Jet Flows #Ultrasonics and Acoustic Wave Propagation #acoustic impedance #acoustic liner #bias flow #double-input describing function #nonlinear acoustic resistance #perforated plate #two-tone excitation
paper · doi:10.14279/depositonce-24711
openalex publication_date 2025/06/18 · openalex created_date 2025/11/06 · openalex updated_date 2026/07/01
This study addresses theoretically and experimentally the combined effects of a bias flow, a high-amplitude primary acoustic field and a high-amplitude secondary harmonic excitation – uncorrelated to the primary excitation – on the acoustic resistance of perforations. The nonlinear acoustic resistance is derived from unsteady Bernoulli’s principle, with the common assumption that the instantaneous pressure loss is proportional to the kinetic energy. The acoustic pressure loss coefficient is assumed constant over time. In the frequency domain, the resulting expression for the resistance is the product of the acoustic pressure loss coefficient and an analytically-derived effective velocity. An explicit formula is obtained which is very accurate for any value of the velocity ratios by adopting a double-input describing function approach. To assess the theory, experiments are performed in a normal-incidence acoustic test-rig, with a steady bias flow and high-amplitude acoustic forcings at two frequencies. The theory is also compared with existing data obtained for two high-amplitude acoustic forcings in the absence of bias flow. For each perforated plate characterised experimentally it is found that the pressure loss coefficient scales with a single Strouhal number, which is based on the analytically derived effective velocity, regardless of how the two acoustic velocity amplitudes and the steady velocity compare to each other.