随着凝聚态物理中拓扑效应的发现，在经典的声学领域中开拓了一个新的研究方向——拓扑声学材料。它可以引导声波在任意路径上鲁棒性传输，且不受材料本身缺陷的影响，这对于声通信和新型声学器件的研发都具有十分重大的意义。虽然拓扑声学人工材料的提出为声波的传输与控制提供了新的方法和理论，但其本身也存在着一些局限性。拓扑声学材料的构造多基于被动声学材料，造成系统的工作频带窄且固定。另外，实现拓扑声学材料的拓扑效应大多依赖于特定的晶格对称性和几何结构参数，这较大程度的限制了拓扑声学材料的设计。对于大多数高阶拓扑声学材料，其仅能实现单一的角态模式分布，难以实现多种类型角度的角态分布，使得拓扑声学材料的应用场景受到限制。因此，围绕以上拓扑声学材料存在的问题，本文开展了以下研究：

1、实现了宽频灵活操控的拓扑声学系统。基于六边形蜂窝状穿孔结构，引入面外方向高度自由度，使得系统的几何构型可以被重构。通过改变孔洞中水柱的高度改变结构几何构型，实现对拓扑声学材料色散曲线的调节。基于量子谷霍尔效应实现拓扑相变，在拓扑带隙处产生边界态的色散曲线。且边界态色散曲线也随着液柱高度变化而变化，使得拓扑边界态可以在较宽的频率范围内进行变化，实现了宽频灵活操控的拓扑声学系统。

2、设计了不依赖于狄拉克锥破缺机制的非对称手性螺线结构。采用非对称的阿基米德螺线结构，构造了手性谷拓扑声学材料。通过探究螺线相关几何结构参数与谷陈数之间的变化关系，获得了影响拓扑相变的重要几何参数。基于此，构造了具有相反陈数的谷霍尔相左旋右旋螺旋结构，在拓扑边界处实现了鲁棒传输的边界态。另外基于转角与拓扑相变间的关系，构造了一种声学开关的结构，为声信号的传输与控制提供了新的方法。

3、实现了多种类型的角态分布模式。基于手性风车结构构造了拓扑四极子单元，在拓扑带隙处不仅产生了有带隙的边界态，还产生了带隙内角态的能量分布模式。调节结构单元的几何参数，研究了系统体、边、角态随几何参数变化的演化情况。另外在直角梯形声学超晶格结构中实现了多种类型的角态模式分布，丰富了声能量传输模式。

4、设计了编码超表面并实现了焦点能量可调的效果。根据编码的设计方法构造了能量可调的聚焦声学超表面。将双开口的赫姆霍兹共振单元与无色散的声通道单元结合，构成0-π相位差，组成“0”、“1”编码单元，然后根据聚焦超表面的相位分布函数进行排列组合。实现了对平面声波的宽频聚焦功能，且通过移动共振腔间的隔板可实现对焦点能量调节功能。

论文的创新点为：

1、提出了一种主动调控拓扑声学系统色散曲线的方法。通过连续的改变拓扑系统中的水量，可以使得拓扑边界态也发生连续的变化，也极大的拓宽了拓扑系统的工作频率范围，对于拓扑声学系统的实际应用具有重要意义。

2、提出了一种不依赖于狄拉克锥破缺机制的手性拓扑声学结构。考虑到基于狄拉克锥破缺机制的拓扑系统对结构单元严格的对称性要求，采用具有低对称性的手性螺线结构实现了拓扑传输特性，简化了拓扑系统的结构单元设计。

3、提出了一种可实现多种类型角态能量分布的高阶拓扑结构。采用手性风车结构构造了具有多种拐角形状的直角梯形超晶格，实现了多种类型角态能量的分布，丰富了声能量的传输模式。

With the discovery of topological effects in condensed matter physics, a new research direction has been poineered in the classical acoustic field — topological acoustic materials. Being able to steer the acoustic waves for robust transmission on arbitrary paths and independent of defects in the material itself, it is of great significance for both acoustic communication and the development of new acoustic devices. Although the proposed topological acoustic artificial material provides a new method and theory for the transmission and control of acoustic waves, there still exist some limitations. The configuration of topological acoustic materials is mostly based on passive acoustic materials, causing the system to operate in a narrow and fixed frequency band. Furthermore, the topological effects are mostly dependent on specific lattice symmetry and geometrical structure parameters, which limit the design of topological acoustic materials to a considerable extent. For most of the higher-order topological acoustic materials, only single corner state mode distribution can be realized, making it difficult to realize various types of corner state distribution, so that the application scenarios of topological acoustic materials are limited. Therefore, regarding the above problems of topological acoustic materials, the following researches are carried out in this dissertation.

1. A topological acoustic system with a broadband flexible manipulation is realized. Based on the hexagonal honeycomb perforated structure, the height degree of freedom in the out-of-plane direction is introduced, allowing the geometric configuration of the system to be reconfigured. The geometric configuration of the structure can be changed by altering the water column height in hole to adjust the dispersion curve of the topological acoustic material. The topological phase transition is realized based on the quantum valley Hall effect, which generates the dispersion curve of the boundary state at the topological band gap. And the boundary state dispersion curve also varies with the height of the liquid column, making the topological boundary state changeable over a wide frequency range. A topological acoustic system with flexible manipulation over a wide frequency range is realized.

2. An asymmetric chiral spiral structure that does not depend on the Dirac cone breaking mechanism is designed. The chiral valley topological acoustic materials are constructed adopting the asymmetric Archimedean spiral structure. The key geometrical parameters affecting the topological phase transition are obtained by investigating the variation relationship between the geometrical structure parameters related to the spiral and the valley Chern number. Based on this, the left-handed and right-handed spiral structure with the opposite valley Hall phases characterized by opposite Chern numbers are constructed, and the boundary state of robust transmission is realized at the topological interfaces. In addition, based on the relationship between the rotation angle and the topological phase transition, an acoustic switching structure is constructed, which provides a new method for the transmission and control of acoustic signals.

3. Various types of corner state distribution modes are realized. A topological quadrupole unit is constructed based on the chiral windmill structure, which generates not only the gapped boundary states at the topological band gap, but also the corner states within the band gap. The geometrical parameters of the structural unit are adjusted and the evolution of the bulk, edge and corner states with the change of geometrical parameters is investigated. In addition, various types of corner state mode distributions are realized in the right-angle trapezoidal acoustic superlattice structure, enriching the acoustic energy transfer modes.

4. Coding metasurface is designed and the focal energy can be adjustable. The focused acoustic metasurface featured tunable energy is constructed based on the coding method. The double-opening Helmholtz resonant unit and the nondispersive acoustic channel unit are combined to create a 0-π phase difference to form a "0" and "1" coding unit, which is then arranged and combined according to the phase distribution function of the focused metasurface. The broadband focusing in terms of plane acoustic wave is realized, and the focal energy adjustment function can be realized by moving intermediate plate of Helmholtz resonator.

The innovation of this dissertation is as follows.

1. An active method of regulating dispersion curve of topological acoustic system is proposed. By continuously altering the water volume in the topological system, the dipersion of topological boundary state can be continuously changed, which also greatly widens the operating frequency range of the topological system and is of great significance for the practical application.

2. A chiral topological acoustic structure that is independent of the Dirac cone breaking mechanism is proposed. Considering the strict symmetry requirement for the structural unit of the Dirac cone breaking mechanism based topological system, a chiral spiral structure with low symmetry is used to realize the topological transmission characteristics and simplify the structural unit design of the topological system.

3. A high-order topological structure that can hold various types of corner states is proposed. A right-angle trapezoidal superlattice with various corner shapes is constructed by the chiral windmill unit cell to realize various types of corner states energy distribution and enrich the transmission modes of acoustic energy.