High sound pressure level sound absorption in acoustic resonant metamaterials: adapting a mass-spring model for nonlinear effects

In aerospace, conventional materials as micro-perforated panels backed by cavities are used to absorb sound at high sound pressure levels. These solutions are not optimal at low frequencies compared to resonant acoustic metamaterials, which present an acoustic absorption peak with a wavelength-to-thickness ratio greater than conventional materials, i.e., a ratio>>5. Acoustic resonant metamaterials are mainly studied at low sound pressure levels (<100dB). However, they are sensitive to increasing the amplitude of acoustic excitation. The studied metamaterial is composed of a compact array of thin single-perforation panels spaced by thin cylindrical air cavities. In a previous study, a mass-spring model was developed for low sound pressure levels. The perforations are modeled by equivalent masses, whereas cavities by equivalent springs. In the perforations, high values of the acoustic velocity lead to an increase in the acoustic resistance of the material. This effect is considered by the Forchheimer parameter in the mass-spring model. To determine this parameter and to study how it is impacted by the metamaterial geometry, the computational fluid dynamic method is used. The mass-spring model is adapted with a nonlinear term. The adapted model agrees well with simulations by finite element method at sound pressure levels up to 140dB.