We propose a dual-frequency anti-nonlinear sound-absorbing metasurface (DASM) based on multilayer nested microslit resonators. Under the assumption of a linear system, the theoretical acoustic impedance of the DASM is derived by the transfer matrix method. Furthermore, the influence of structural parameters on sound absorption is also explored. The numerical and experimental results show that the proposed DASM can achieve quasi-perfect sound absorption at two low frequencies corresponding to the first two orders of the acoustic cavity mode frequencies of the structural unit, and enjoys strong anti-nonlinear performance and robustness to incident angles.

The low-frequency harmonic components of urban substation noise are easy to annoy the residents. Multi-frequency perfect sound-absorbing metasurface based on the Helmholtz resonator (HR) is an alternative solution to suppress the low-frequency harmonic noise. This paper proposes an efficient design method of structural parameter for the multi-frequency perfect sound-absorbing metasurface. Taking the perfect sound absorption at the target frequency as objective and the structural parameters of HR as optimization variables, the structural parameter optimization model of multi-frequency perfect sound-absorbing metasurface is established and solved by the sequential quadratic programming algorithm. The proposed design method effectively overcomes the deterioration of sound absorption performance caused by the combined design of multiple perfect sound absorption units. Utilizing the proposed method, we designed a multi-frequency perfect sound-absorbing metasurface to absorb the four harmonic components of an urban substation noise simultaneously. The finite element simulation results and the experimental results of the physical sample indicate that the designed multi-frequency perfect sound-absorbing metasurface can satisfy critical coupling to achieve perfect sound absorption at all target frequencies.