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• Complex frequency plane quantifies metamaterial loss at linear sound levels. • Prediction of trends in absorption coefficient changes at high sound levels. • Experimental validation for multi-resonant metamaterials with varying loss levels. • Identifying profiles with improved high sound level absorption at high sound levels. This study proposes using the complex frequency plane representation as a tool to quantify loss levels of a metamaterial at low sound levels, enabling the prediction of trends in absorption coefficient changes at high sound levels. A multi-resonant metamaterial composed of a series of thin annular cavities connected by a central perforation is considered which has been previously studied in the linear regime. With the analytical model developed for the linear regime, the representation of the complex frequency plane allows understanding whether a low value of absorption peak is due to excessive losses or, instead, to a lack of losses in the material. As sound level increase, material losses rise, leading to decrease in absorption peaks for structures with excessive losses and increase of peak absorption coefficient values for those with insufficient losses. Multi-resonant metamaterials with a constant main pore profile are selected to exhibit resonances with various loss levels, and measurements in a high sound level impedance tube are conducted to validate the expected changes in absorption coefficient. After that, an acoustic black hole is considered and a structure with two low frequency absorption peaks increasing with sound level and presenting a broad absorption band with low sensitivity to high sound levels is identified. The predictions are validated experimentally.
Bezançon et al. (Sat,) studied this question.