Mass-spring model for a perforated periodic metamaterial in nonlinear regime

This study is interested in the nonlinear acoustic response of a metamaterial composed of a periodic array of single-perforation plates spaced by thin air cavities. An equivalent mass-spring model is adapted to predict the metamaterial acoustic response under high sound pressure levels. The increase in losses induced by the high level is considered by a quadratic law for the airflow resistivity in an effective fluid model. The airflow resistivity coefficients are determined from predictions by the computational fluid dynamics method at different flow velocities. The model is validated with impedance tube measurements for samples with different numbers of periodic unit cells and perforation sizes. The results show that the acoustic resistance of the metamaterial increases with increasing sound pressure levels, while the reactance is almost unchanged. The absorption peaks at low frequencies are more impacted by high sound pressure levels. A criterion based on the viscous characteristic frequency is proposed to determine the limit of the beginnings of the nonlinear material response. This limit is given by an acoustic Reynolds number, which depends on the frequency and perforation size. Experimentally, an absorption peak is observed, shifting to lower frequencies with increasing sound levels. A preliminary explanation of underlying mechanisms is provided.