减振降噪在工业发展和日常生活中具有迫切的应用需求。负刚度和负泊松比力学超材料因其反常的物理特性和独特的变形机制，在振动控制、缓冲吸能等领域展现出巨大的应用潜力。目前传统的被动式隔振力学超材料一经构建，其性能基本确定，无法满足可调控性能结构的需求。而主动调控隔振式的力学超材料又对基体材料和服役环境有着严苛的要求，并且造价高昂，应用过程中还需要持续维持电磁场或温度场的激励。因此，亟需开展方便、快捷且实用的可调减振降噪特性力学超材料研究。本文立足于此，进行了具备可调隔振性能的负刚度和负泊松比力学超材料的结构设计、力学特性分析、波动特性分析等一系列工作。

首先利用负刚度结构中典型的双稳态弯曲梁胞元，设计了六角型的负刚度双稳态结构，其沿z轴方向展现出双稳态特性。通过数值分析方法研究了结构几何参数和双稳态性能之间的关联，得到了两者之间的相图，明确了具备双稳态性能的结构几何形态。随后，针对具备双稳态特性的结构开展了不同构型之间的隔振性能仿真研究。计算结果显示，不同构型下的结构其带隙的位置和范围均存在一定的差异，同时调整几何参数也可以调控结构的隔振特性。

在单向双稳态特性结构的研究基础上，开展了双向双稳态特性的多稳态弹性波超材料研究。该结构在x，y轴方向均展现出双稳态性能，使得整体结构具备多个稳定构型。通过准静态拉伸仿真及测试，验证了结构的多稳态特性，并对不同构型进行了编码化处理。振动模态分析显示，结构的带隙产生机制为局域共振。能带结构计算和传输特性测试证明结构具有可调的隔振性能。同时，利用数字编码处理的单胞结构进行了周期性波导装置的拓展应用研究，构建了18×18的周期性波导，成功实现了弹性波的定向传输。

为进一步提高结构的隔振能力，在负刚度机制的可调隔振性能力学超材料研究的基础上，引入了负泊松比结构。旨在利用负泊松比结构独特的变形机制来增强结构的隔振能力，并扩大其可调控范围。基于内凹形负泊松比结构设计了双负力学超材料，以负刚度行为为指标，分析其几何参数对结构力学特性的影响；以传输特性系数为指标，分析其结构构型对整体隔振特性的影响。研究发现通过几何参数调整和稳定构型转变都可以实现对结构的隔振特性进行实时调控，利用不同构型的单胞结构构建了不同频段的弹性波屏蔽装置。

基于星形负泊松比结构结合负刚度双稳态弯曲梁进行了可调隔振性能的力学超材料设计，相比于内凹形双负超材料结构，星形双负超材料结构具备更多的稳定构型，可以提供更多调控选择。研究首先验证了结构的双稳态特性，后续研究了结构的振动模态和波动特性。相比于负刚度双稳态结构，引入了负泊松比独特变形机制的超材料具备旋转变形引发的局域共振机制，结构具备了新的带隙，其隔振能力得到进一步加强。

在本文中，利用力学超材料中典型的负刚度机制和负泊松比机制结构设计了多种结构形式的弹性波力学超材料。结构稳定构型的转变为实时调控结构隔振特性提供了一条切实可行的道路。而且结构的负刚度、负泊松比行为均可以增强其隔振特性，同时这些结构还具备多种变形模式，可以满足不同的工况需求。

Vibration and noise reduction are crucial in both industrial development and daily life. Mechanical metamaterials featuring negative stiffness and negative Poisson's ratio mechanics exhibit remarkable potential for applications in vibration control, shock absorption, and energy dissipation, owing to their exceptional physical characteristics and unique deformation mechanisms. While traditional passive vibration isolation mechanical metamaterials provide fixed performance upon construction, they fall short of meeting the demand for tunable structural performance. On the other hand, active vibration isolation mechanical metamaterials require specific matrix materials and operational conditions, resulting in increased costs and the need for ongoing maintenance of electromagnetic or thermal field excitation. Hence, there exists an urgent need for convenient, expeditious, and practical research on mechanical metamaterials with tunable vibration and noise attenuation capabilities.

Firstly, a hexagonal negative stiffness bistable structure is designed utilizing the conventional bistable bending beam cell element within negative stiffness structures, exhibiting bistable characteristics along the z-axis orientation. The correlation between structural geometrical parameters and bistable attributes is investigated through numerical analysis, leading to the generation of phase diagrams identifying geometric configurations with bistability. Subsequent simulation studies assess the vibration isolation effectiveness of structures with bistable traits in various arrangements, revealing variations in bandgap position and extent across diverse structures. Furthermore, it is demonstrated that adjusting the geometric parameters enables manipulation of the vibration isolation performance of these structures.

Expanding upon previous research on unidirectional bistable structures, this study explores multistable elastic wave metamaterials with bidirectional bistable features. The structure showcases bistability in both x- and y-axis directions, resulting in multiple stable configurations. Quasi-static tensile simulations and tests verify the multistable nature of the structure, capturing its various configurations. Vibration modal analysis reveals that the structure's bandgap generation stems from local resonance. Additionally, band structure calculations and transmission characteristic tests showcase the tunable vibration isolation performance of the structure. Notably, leveraging digitally encoded and processed single-cell structures, the study broadens the application of periodic waveguide devices, an 18 x 18 periodic waveguide was manufactured, successfully achieving directional transmission of elastic waves.

To enhance the vibration isolation capabilities of the structure, negative Poisson's ratio structures are introduced based on the research on tunable vibration isolation performance with negative stiffness mechanism in mechanical metamaterials. This approach utilizes a unique deformation mechanism to expand the range of tunable control and improve the vibration isolation capability of the structure. By employing the re-entrant negative Poisson's ratio structure, a double-negative mechanical metamaterial was designed to assess the influence of its geometric parameters on the structural mechanics. The negative stiffness behavior has been used as an index to measure this impact. Furthermore, the influence of the structural configuration on the overall vibration isolation characteristics has been analyzed using the transmission characteristic coefficient as an index. The adjustment of geometrical parameters and stabilization of the configuration transformation can enable real-time regulation of the vibration isolation characteristics of the structure. Additionally, elastic wave shielding devices of different frequency bands can be constructed using single-cell structures of varying configurations.

The design of mechanical metamaterial for tunable vibration isolation performance involves the integration of a star-shaped negative Poisson's ratio structure with a negative-stiffness bistable bending beam. This innovative approach provides a broader range of stabilizing configurations and tuning possibilities compared to the re-entrant double-negative metamaterial structure. The research validates the bistable characteristics of the design and subsequently investigates its vibrational modes and fluctuation properties. In contrast to the negative-stiffness bistable structure, metamaterials utilizing the unique deformation mechanism of negative Poisson's ratio demonstrate a local resonance phenomenon triggered by rotational deformation, leading to the emergence of a novel bandgap that enhances their vibration isolation capabilities.

This paper introduces the design of elastic wave mechanical metamaterials featuring multiple structural configurations utilizing negative stiffness and negative Poisson's ratio mechanisms, both common in mechanical metamaterials. The alteration of structural stability configurations offers a viable approach for dynamically adjusting the structural vibration isolation properties in real-time. Furthermore, the incorporation of negative stiffness and negative Poisson's ratio characteristics in these structures enhances their vibration isolation capabilities. Additionally, these structures exhibit multiple deformation modes to accommodate diverse operational scenarios.