This research is focused on the acoustic efficiency of various shapeHelmholtz resonators on non-linear operating modes, with an acoustic pressure level of 130 dB. In this work physical and mathematical models for predicting the effective acoustic properties of SAS cells are formulated. Numerical studies have been performed to assess the acoustic efficacy of honeycomb and cone-shaped sound-absorbing structures samples in an interferometer with a normal incidence of a sound wave in a nonlinear operation mode. The validation of the developed mathematical models was carried out. A comparison of the numerical calculation results with the results of laboratory studies has been carried out. According to the results of the conducted computing experiments, the most effective resonators were identified, and recommendations on the SAS design based on the most effective resonators were formulated.