声学超构材料(Acoustic Metamaterials, AMs) 是一种由人工设计微结构单元组成的复合材料，其结构单元尺寸远小于声波波长，且拥有许多自然材料所不具备的奇异特性，如声聚焦、声吸收、超透镜、声隐身和振动隔声等。现有的三维核壳结构、二维薄膜结构以及一维“超原子”型负质量密度声学超构材料的结构单元虽满足了多频以及可调谐的需求，但仍存在结构复杂、尺寸庞大以及结构体脆弱等缺陷。针对这一现状，本论文提出了嵌套型多频带负质量密度声学超构材料以及基于内嵌开孔隔板U型空心管的双频带负质量密度声学超构材料，它们既可以在同频率下减小结构尺寸，同时还具有用一个结构单元在多个频带实现负质量密度的优势。论文的主要工作涉及以下三个方面：

（1）基于之前课题组嵌套多层空心球的研究思路，本论文提出一种嵌套型多层半开半闭 (Open End-Close End, OE-CE)空心圆管(NMLHT)的多频带可调谐负质量密度声学超构材料（AMs），运用有限元仿真软件研究了不同层数、不同管径和不同水介质高度对多层OE-CE空心圆管的声透射性能的影响规律。结果表明：改变结构单元层数能够调控负等效质量密度频带个数，其中频带个数与嵌套层数相等；同时调整NMLHT的管径以及管腔内水介质的高度能够调控负等效质量密度的频带位置，其谐振频率与管径成反比，与管腔内水介质高度成正比。另外，结合驻波共振原理和耦合效应理论推导出NMLHT谐振频率的精准计算公式，该理论计算频率与仿真结果相一致。

（2）本文提出了一种嵌套型双层OE-CE管(NDLHT)的双频带可调谐负质量密度声学超构材料（AMs），它是通过调整内外层管长或管径来实现调控负等效质量密度的频带。利用有限元仿真软件对不同管长和不同管径的双层OE-CE空心圆管的声透射性能进行仿真模拟，详细研究了管长与管径对该超构材料谐振频率的影响规律。结果表明：在内层管长大于外层管长的条件下，该超构材料存在两个谐振频率，且在两个谐振频率附近均实现了负的等效质量密度。改变内外层管长或管径均会实现对谐振频率主动调控。其中，管长对负等效质量密度频带的调控幅度大于管径，且仿真结果与理论结果吻合很好。

(3) 本文提出了一种内嵌开孔隔板的双频带U型空心管声学超构材料。首先研究了未内嵌开孔隔板的U型管的管长、管径和管口间距对该超构材料的声学性能的影响规律，进一步构建了不同开孔隔板嵌入位置的三种U型管声学超构材料模型，仿真研究了其隔板的开孔半径和隔板厚度对该超构材料透射性能的影响规律。结果表明：U型空心管的谐振频率随管长与管径的增大而减小，随管口间距的增大而增大；当开孔隔板位于对称位置时，均只有一个谐振频率，非对称位置时均出现两个谐振频率，且谐振频率值随隔板开孔大小的增大而增大，随隔板厚度的增大而减小。

Acoustic Metamaterials (AMs) are composite materials composed of artificially designed microstructural units, has a structural unit size much smaller than the wavelength of sound, and possesses many exotic properties that are not found in natural materials, such as acoustic focusing, acoustic absorption, super-lensing, acoustic cloak, and vibrational sound insulation. The existing AMs with negative mass density have some disadvantage of structural complexity, large size and fragility of the structure, although they can satisfy the needs of multi-frequency and tunability. To address these problems, this thesis proposes a nested type of multi-band acoustic metamaterials with negative mass density and dual-band U-shaped hollow tube acoustic metamaterials with embedded open-ended spacer, which not only can reduce the structural size at the same frequency, and but also have the advantage of realizing the negative mass density in multiple bands with a single structural unit. The main work of the thesis includes the following three aspects:

(1) Similiar to the research idea of nested multilayer hollow spheres with negative modulus in our research group, this thesis presents multi-band tunable acoustic metamaterials with negative mass density based on a nested multilayer half-open-half-closed (Open End-Close End, OE-CE) hollow tubes (NMLHT), and the effects of different number of layers, different tube diameters, and different heights of water medium on the sound transmission performance of the multilayer OE-CE hollow circular tubes were investigated by finite-element simulation software.  The results show that: changing the layers number of structural unit can regulate the number of frequency bands with negative mass density, in which the number of frequency bands is equal to the number of nested layers. The position of the frequency bands of negative mass density can be modulated by adjusting the diameter of the NMLHT and the height of the water medium in the cavity. The resonant frequency is inversely proportional to the pipe diameter, and directly proportional to the height of the water medium. In addition, the precise formula for the resonant frequency of NMLHT is derived by combining the principle of standing wave resonance and the theory of coupling effect, and then the theoretically calculated frequency is consistent with the simulation result.

(2) In this thesis, a dual-band tunable negative mass density acoustic metamaterials (AMs) of nested double-layer OE-CE tubes (NDLHT) is proposed, which is realized by adjusting the inner and outer tube lengths or diameters to tune the frequency band with negative mass density. The acoustic transmission properties of double-layer OE-CE hollow circular tubes with different tube lengths and diameters are simulated by finite element simulation software, and the effects of tube length and diameter on the resonant frequency of this metamaterials are investigated in detail. The results show that the metamaterials has two resonance frequencies under the condition that the length of the inner layer is larger than that of the outer layer, and a negative effective mass density is realized near both resonance frequencies. The resonance frequencies can be regulated by changing the inner and outer tube lengths or diameters, and the simulation results are in good agreement with the theoretical results. In particular, the modulation amplitude of the tube length is greater than that of the tube diameter.

(3) In this thesis, a dual-band U-shaped hollow tube acoustic metamaterials with embedded open-aperture spacer is proposed. Firstly, the effects of the tube length, tube diameter and orifice spacing on the acoustic properties of the U-tube without embedded open-ended spacer were investigated. Three U-tube acoustic metamaterial models with different embedding positions of the open spacer are further constructed, and the effects of the opening radius of the spacer and the thickness of the spacer on the transmittance properties of the metamaterials are investigated in simulation. The results show that the resonance frequency of the U-shaped hollow tube decreases with the increase of the tube length and diameter, and increases with the increase of the orifice spacing; when the open-ended spacer are located in the symmetric position, there is only one resonance frequency, and there are two resonance frequencies in the asymmetric position, and the value of resonance frequency increases with the increase of the hole size of the spacer, and decreases with the increase of the thickness of the spacer.