| Acoustic metamaterials are a kind of synthetic periodic structural materials,which have the advantages of controlling large wavelengths in small size,and it can also control the propagation direction of sound waves,in recent years,there have been new developments and applications in sub-wavelength imaging,bandwidth improvement,filtering,phase correction,focusing,vibration sound insulation and other fields.Based on the idea of local resonance,this paper proposed a multi-band negative modulus acoustic metamaterials,its structural unit was nested by the split hollow spheres with different parameters,based on the acoustic-force analogy principle,the coupling and non-coupling multi-series spring oscillator model was proposed,the transmission performance of the nested multi-band acoustic metamaterials with the opposite direction of the hole from the theoretical analysis and COMSOL software simulation was studied in detail,and the geometric parameter conditions of the nested multilayer structural unit for achieving negative effective elastic modulus were given.The thesis mainly involved the following aspects:(1)In this thesis,the nested two-layer split hollow sphere structure unit was designed,and the calculation formula of the resonance frequency of the two series spring oscillator system was derived based on the sound-force analogy principle,on the other hand,the influence of geometric parameters such as the inner radius of the outermost sphere and the relative size of the two splitting holes on the transmission performance of the nested two-layer acoustic metamaterials was studied by COMSOL finite element simulation software,and the accurate design method of the dual-band negative modulus acoustic metamaterials was initially given from two aspects of theoretical analysis and simulation.The results showed that the transmission absorption peak of the two-layer split hollow sphere appears in the two frequency bands,and the resonant frequency calculated by the theory was basically consistent with the resonance frequency obtained by the simulation.As the two split diameters gradually increased,the two-layer nested SHSs achieved negative effective modulus in both the low and high frequency regions.When the two split diameters are equal and the two split diameters sizes were gradually reduced,the two-layer nested SHSs can achieve negative modulus in the lowfrequency region;and the appropriate a1 in the high-frequency region can easily achieve negative modulus.Therefore,the geometric parameters of negative modulus structural units can be accurately predicted by theoretical formulas,so that dual-band negative-modulus acoustic metamaterials can be actively designed in the desired frequency band.(2)In this thesis,the nested three-layer split hollow sphere structure unit was designed,and the calculation formula of the resonance frequency of the three series spring oscillator system was derived based on the sound-force analogy principle,the calculation formula of the resonant frequency of the derived three-scries spring oscillalor system was combined with the couple interaction,and finally the coupling formula for accurately calculating the resonance frequency geometric parameters such as the inner radius of the outermost sphere and the relative size of the three splitting holes on the transmission performance of the nested three-layer acoustic metamaterial was studied by COMSOL finite element simulation software.The results showed three-layer split hollow spheres have transmitted absorption peaks in three frequency bands.The resonance frequency calculated by the coupled and improved three-series spring oscillator model was basically consistent with the simulated value.When the three holes gradually increased,that is,a1<a2<a3,the nested three-layer split hollow sphere metamaterials can achieve negative effective modulus near the resonance frequency in the low frequency,medium frequency and high frequency region.Under the condition of the largest medium hole,that is,a3<a1<a2,the negative modulus can be achieved near the resonance frequency in the low and medium frequency regions,and the negative modulus near the resonance frequency in the high frequency region required relatively smaller al and a2 or relatively larger a3.At the minimum middle hole diameter,that is,a2<a1<a3,negative modulus can be achieved near the resonance frequency in the low and medium frequency regions,achieving negative modulus near the resonant frequency in the high-frequency region required a relatively larger a3.When the three holes were gradually reduced,that is,a1>a2>a3,the nested three-layer split hollow sphere metamaterials can achieve negative modulus near the resonance frequency in the low and medium frequency regions,but cannot achieve negative modulus in the high frequency region.This thesis got the accurate design methods of three-band negative-modulus acoustic metamaterials from two aspects of theoretical analysis and simulation.(3)In this thesis,the nested four-layer split hollow sphere structure unit was designed,and the calculation formula of the resonance frequency of the four series spring oscillator system was derived based on the sound-force analogy principle,the calculation formula of the resonant frequency of the derived four-series spring oscillator system was combined with the couple interaction,and finally the coupling formula for accurately calculating the resonance frequency of the nested four-layer split hollow sphere was presented.On the other hand,the influence of geometric parameters such as the inner radius of the outermost sphere and the relative size of the four splitting holes on the transmission performance of the nested four-layer acoustic metamaterials was studied by COMSOL finite element simulation software.The results showed four-layer split hollow spheres had transmission absorption peaks in four frequency bands.The resonance frequency calculated by the coupled and improved four-series spring oscillator model was basically consistent with the simulated value.The four-layer SHSs acoustic metamaterials under the condition of gradually decreasing four holes can achieve negative effective modulus near the lower three resonant frequencies region;in the high-frequency region,the metamaterials cannot achieve negative effective elastic modulus.The four-layer SHSs acoustic metamaterial under the condition of gradually increasing four holes can achieve negative effective modulus in the low-frequency,medium frequency,sub-high frequency and high frequency regions,and the larger the a4,the better effect of the negative modulus.The four-layer SHSs acoustic metamaterial with the smallest middle hole and the largest condition of the outermost hole diameters can achieve negative effective modulus near the lower three resonant frequencies;in the highfrequency region,the metamaterial cannot achieve negative effective elastic modulus.Four-layer SHSs acoustic metamaterials with the largest middle hole diameter and the smallest innermost hole diameter achieved negative effective modulus near the two resonant frequencies at the low and medium frequencies regions.Negative effective modulus cannot be achieved in both the subhigh and high frequency regions.In this thesis,the accurate design method of four-band negativemodulus acoustic metamaterials was preliminarily proposed from two aspects of theoretical analysis and simulation. |
