Mechanism analysis and optimal design of sound-absorbing metastructure constructed by slit-embedded Helmholtz resonators

Abstract

Low-frequency noise has always been a thorny problem in the field of noise control. In recent years, the development of sound-absorbing metastructures has provided new ideas for low-frequency noise control. In this paper, we propose low-frequency sound-absorbing metastructures constructed by Helmholtz resonators with embedded slit. Analytical and numerical models were established to analyze the sound absorption performance and mechanism of the proposed sound-absorbing metastructure, and optimization design was conducted to achieve low-frequency wideband absorption performance. The analytical modeling method and the performance of the proposed sound-absorbing metastructure were also experimentally verified. The main conclusions are summarized as follows:<br>1) Based on the use of transfer matrix method and finite element method, analytical and numerical models for calculation of sound absorption coefficient were established. It was shown that analytical predictions are in good agreement with numerical calculations. It was demonstrated that a typical design of a single-cell metastructure with 30mm thickness can achieve a sound absorption coefficient of 0.88 at 404 Hz. Typical designs of two-cell and the four-cell parallel structures (with 50 mm thickness) can achieve two and four near-perfect low-frequency sound absorption peaks within the frequency band of 200-400 Hz, respectively.<br>2) The low-frequency sound absorption mechanisms of the proposed metastructure were explained from four aspects: simplified equivalent model parameters, normalized acoustic impedance, complex-plane zero/pole distribution, sound pressure cloud image and particle velocity field distribution. It was demonstrated that the main sound absorption mechanism is associated with the thermal viscous loss of sound waves caused the inner wall of embedded slit.<br>3) Optimization design for broadband low-frequency absorption performance was carried out by using differential evolution optimization algorithm. A parallel-multi-cell coupled metastructure with multiple perfect sound absorption peaks below 500Hz was optimized. Under the condition of thickness 90mm, the sound absorption coefficient curve of an optimized metastructure exhibited 8 near-perfect sound absorption peaks and an average sound absorption coefficient of 0.86 within the frequency range of 170-380 Hz.<br>4) Experimental samples were fabricated to carry out sound absorption tests. Experimental results were basically consistent with the analytical predictions. Mutual verification of analytical model, numerical calculation and experimental measurements was completed.<br>To sum up, the sound-absorbing metastructures proposed in this paper have outstanding sound absorption performance at low frequencies with sub-wavelength thickness. We demonstrated they are suitable for low frequency broadband sound absorption below 500 Hz. Thanks to their thin thickness and relatively simple construction, they have broad application prospects in practical noise control engineering.