Research On Space Coiling Acoustic Metamaterials Based On Hilbert Fractal Design

Due to its special penetrating ability,low-frequency sound exists in daily life,industrial equipment,military and other aspects,bringing adverse effects on health,product manufacturing and military activities.Considering the mass den sity law,conventional acoustic materials cannot control the low frequency sound propagation well.Acoustic metamaterial is one or more structures or materials with periodic array in a particular way,which achieves special properties that are not found in natural materials,such as acoustic band gap,negative refraction,near zero-refractive index et al.It provides a new solution for great potential,like low frequency noise reduction,ultrasonic imaging and sound cloaking and tunneling.Among them,space coiling acoustic metamaterials have become the focus of acoustic metamaterials because of their low dissipation,simple structure and strong reflection.The study of wave propagation behavior in acoustic metamaterials is of great academic value and has important guiding significance for acoustic devices and engineering applications.Inspired by nature fractal,the self-similar fractal technology is applied to the design of space coiling acoustic metamaterial,construct a class of fractal space coiling acoustic metamaterials,focusing on its physical mechanism and application,etc.,through the band theory,effective medium theory and finite element simulation,systematically studied the fractal on the effect of space coiling acoustic metamaterial,such as band gap,near zero-refractive index and effective,etc.,and the main contents are:(1)The self-similar fractal design was introduced into the space coiling acoustic metamaterial to obtain the multi-band gap at the sub-wavelength scale.In view of the sub-wavelength and multi-band characteristics of the Hilbert fractal curve in the optical field,a two-dimensional Hilbert fractal acoustic metamaterial structure is proposed in this paper.It is found that with the increase of Hilbert fractal order,the effective refractive index of Hilbert fractal metamaterials increases,while the effective phase velocity of sound waves decreases.The acoustic states and eigenfrequency of Hilbert fractal acoustic metamaterial are systematically studied.The results show that HFAM can generate abundant acoustic states.With the increase of fractal order,not only more bandgap is generated,but also bandgap gradually shifts to high frequency and low frequency regions.The transmission spectrum of finite period Hilbert structure is computered to prove the correctness of the band structure of Hilbert fractal acoustic metamaterial.Then,the transfer function analysis of Hilbert fractal acoustic metamaterial is carried out,and it is found that it has the properties of multi-band acoustic filtering and sound blocking.Finally,the acoustic transfer function analysis of the higher-order Hilbert fractal acoustic metamaterial under the conditions of horizontal,vertical,rotating and their combination are carried out to prove that they still have good robustness under various perturbations.(2)To prove the multi-pole mode characteristics of the two-dimensional Hilbert fractal acoustic metamaterial,the pressure amplification value of the central region of the structure was calculated to verify.Based on the theory of effective medium,the transfer matrix method is used to calculate the effective parameters of two-dimensional Hilbert fractal acoustic metamaterials,namely the effective mass density and bulk modulus.The results show that the fractal structure can generate the negative effective parameters of the multi-band,and the negative effective parameters of the higher-order structure gradually move to the low-frequency domain.In addition,the calculation and analysis of the effective mass density of the acoustic metamaterial plate by the S-parameter method show that,besides zero mass density,coupling resonance between single cells also produces high transmission.The former has zero-phase-difference,while the latter does not.Finally,the study of acoustic radiation field with negative effective parameters and near-zero mass density proves that two-dimensional Hilbert fractal acoustic metamaterials can realize acoustic reflection under sparse arrangement,sound bending transmi ssion,acoustic cloaking and acoustic tunneling.(3)Based on the feature of three-dimensional Hilbert fractal curve,and combining with the design of two-dimensional Hilbert fractal acoustic metamaterial,a three-dimensional Hilbert fractal acoustic metamaterial was designed to realize the free propagation of sound waves in three-dimensional space,with a high effective refractive index and gradually reduced phase velocity.Through the analysis of its band structure,eigenstates and transmission spectrum,it is found that the three-dimensional Hilbert structures can more easily excite the acoustic modes,such as monopolar,bipolar and quadrupolar,and have the characteristics of isotropy in the considered frequency range.The effective parameters of three-dimensional Hilbert structures were analyzed by using the effective medium theory.Compared with the two-dimensional structures,it was found that the three-dimensional structures produced more band gaps,and the frequency corresponding to the lowest band g ap was ultralow in the deep subwavelength scale.Meantime,note that the multi-band comes from the Fabry-Perot resonances,which realizes the characteristic of regulating long wavelength with small size.(4)Considering the influence of thermo-viscous effect on the sound transmission of the space coiling acoustic metamaterial,we designed a labyrinthine fractal acoustic metamaterial.Through the band structure,it is found that the negative bulk modulus generated corresponds to the first frequency band,whi le the negative mass density corresponds to the second frequency band.In the corresponding frequency band,the acoustic modes of labyrinthine metamaterials are consistent with the monopole and bipolar resonances.Through the analysis of the curves of the first frequency band,it is found that there are also isotropic characteristics in this range.The effective parameters of the structure were further studied,and it was found that the structure not only had negative effective parameters,but also had nega tive properties of multi-band.When the thermo-viscous effect is considered,the negative equivalent band and resonance frequency shift slightly to the left.In this paper,the research and discussion on the novel acoustic properties of fractal space coiling acoustic metamaterials are presented,which provide important theoretical guidance for acoustic manipulation.