Mass-spring model for a perforated periodic metamaterial in nonlinear regimea)

Area of Science:

• Acoustics
• Materials Science
• Fluid Dynamics

Background:

• Metamaterials offer unique acoustic properties.
• Understanding nonlinear acoustic response is crucial for high sound pressure level applications.
• Periodic structures with air cavities present complex acoustic behaviors.

Purpose of the Study:

• To investigate the nonlinear acoustic response of a single-perforation plate metamaterial.
• To develop and validate a model predicting acoustic behavior under high sound pressure levels.
• To establish a criterion for identifying the onset of nonlinear material response.

Main Methods:

• An equivalent mass-spring model incorporating a quadratic airflow resistivity law was adapted.
• Computational fluid dynamics (CFD) determined airflow resistivity coefficients.
• Impedance tube measurements validated the model across various configurations.

Main Results:

• Metamaterial acoustic resistance increases with sound pressure level; reactance remains largely unchanged.
• High sound pressure levels significantly affect low-frequency absorption peaks.
• An acoustic Reynolds number criterion was proposed to define the nonlinear response limit.

Conclusions:

• The study successfully models and validates the nonlinear acoustic response of the metamaterial.
• A new criterion based on acoustic Reynolds number helps predict nonlinear behavior.
• Observed low-frequency absorption peak shifts provide insights into underlying physical mechanisms.