Low-frequency noise absorbers often require large structural dimensions, constraining their development in practical applications. In order to improve space utilization, an acoustic metamaterial with a spatial double helix, called a spatial double helix resonator (SDHR), is proposed in this paper. An analytical model of the spatial double-helix resonator is established and verified by numerical simulations and impedance tube experiments. By comparing the acoustic absorption coefficients of the spatial double-helix resonator, it is shown that the results of the analytical model, the numerical model, and the experiments are in good agreement, proving the accuracy of the theoretical model. The effects of different structural parameters on the peak sound absorption coefficient and resonance frequency are quantitatively revealed. The impedance variation law of the model is obtained, and the resistance and reactance distributions at the resonance frequency are analyzed. In the optimization model, the Back Propagation (BP) network is used to construct the mapping between the structural parameters and the resonance frequency and sound absorption coefficient, and this is used as the constraints of the equation, which is combined with Wild Horse Optimization (WHO) to establish the BP-WHO optimization model to minimize the volume of the spatial double helix resonator. The results show that, for a given noise frequency, the optimized structural parameters enhance the space utilization without affecting the performance of the space double helix resonator.

In many noise scenarios, it is necessary to ensure ventilation and noise suppression. In this paper, a ventilated acoustic metamaterial labyrinth plate (VAMLP), formed by an array of labyrinth cells (LCs), is presented. Each labyrinth cell contains four labyrinth waveguide units (WUs). Based on the impedance series principle, an analytical model of the WU was developed and validated by a numerical model and impedance-tube experiments to determine the sound transmission loss of the WU and the LC. The mechanism of the influence of thermo-viscous loss was quantitatively analyzed, and it was clarified that the VAMLP produced sound absorption due to thermo-viscous loss. The change law of impedance at the entrance of the waveguide was analyzed, revealing the noise-reduction mechanism of the labyrinth unit. Combining a BP network and an improved sparrow search algorithm (ISSA), a BP–ISSA optimization model is proposed to optimize the ventilation capacity of the labyrinth cells. The BP-network model can accurately predict the resonance frequency from the structural parameters to form the fitness function. The ISSA optimization model was constructed using the fitness function as the constraint of an equation. Finally, the combination of structural parameters with optimal ventilation capacity was obtained for a given noise frequency.