声学人工材料是一类能够对弹性波进行调控的人工复合材料,在减振降噪、声学隐身、声波导引、声学聚焦和成像等领域有广阔的应用前景。本文结合数值仿真、理论分析及机器学习方法，对带涂层球形夹杂声学超材料和层状声子晶体两种典型声学人工材料的能带计算及设计进行了系统的研究。主要研究成果包括：建立了用于衰减脉冲波的声学超材料设计方法，基于局域共振原理设计了含带涂层球形夹杂的声学超材料，实现有效衰减脉冲波能量。基于传输系数计算和时域模拟验证了超材料对谐波的衰减性能，证实了傅里叶变换方法用于脉冲波频谱分析并针对性地设计禁带的可行性。揭示了夹杂颗粒的几何和物理参数、基体的粘弹性对衰减性能的影响规律，发现禁带宽度的增大可以有效地提高衰减性能，而加入基体材料的粘弹性反而减弱衰减效果。基于层状声子晶体传输系数和能带结构的理论解，揭示了层状声子晶体传输系数与层数、层厚、层序和波长之间的关系，证明了双组元双层单胞的声子晶体材料可实现的禁带范围。理论证明了当材料厚度给定时，增加层数会使衰减效果先增加后减小；当各层材料给定时，层序颠倒不影响传输系数，而将阻抗差异大的材料组合能在整体上实现较好的衰减效果；基于能带结构的理论解，揭示了在材料给定时，双层单胞的声子晶体可实现的禁带范围，且实现最大相对禁带宽度的条件为体积比等于波速比。发展了基于监督学习和强化学习的声学人工材料反向设计新方法，实现了声学超材料、层状声子晶体的最大化禁带宽度和指定禁带的反向设计。基于监督学习实现了二维圆形夹杂的声学超材料的反向设计，证实了以参数作为神经网络输入的可行性并拥有减小数据规模、可以利用先验知识的优点，实现了声学超材料禁带的高精度预测，并通过对神经网络进行遍历来实现快速的反向设计；基于强化学习实现了层状声子晶体一阶禁带宽度最大化和指定禁带范围的反向设计，分析了演化路径的特点，证明了强化学习的探索高效性。所建立的强化学习和力学仿真的交互式框架能够方便地用于其它的力学设计问题。本研究结合有限元模拟和机器学习初步探索了声学人工材料声学特性和其物理、几何参数之间的潜在关系，研究成果将为未来声学人工材料更广泛的应用和更灵活的设计奠定一定的基础。

Acoustic artificial material is a kind of artificial composite material which can control elastic waves. It has a wide application prospect in the fields of vibration reduction, noise reduction, acoustic stealth, acoustic guidance, acoustic focusing and imaging. Based on numerical simulation, theoretical analysis and machine learning method, the band gap calculation and design of two typical acoustical artificial materials, i.e. coated spherical inclusions and layered phononic crystals, are systematically studied in this paper. The main research results include:Based on the principle of local resonance, an acoustic metamaterial with a coated spherical inclusion is designed to effectively attenuate the pulse wave energy. Based on the transmission coefficient calculation and time-domain simulation, the attenuation performance of metamaterials on harmonic waves is verified, and the method of Fourier transform method for pulse spectrum analysis and band gap design is proved to be feasible. The effects of geometrical and physical parameters of inclusions and viscoelasticity of matrix on the attenuation performance are revealed. It is found that the increase of band gap width can effectively improve the attenuation performance, while the viscoelasticity of matrix material may weaken the attenuation effect.Based on the theoretical solution of the transmission coefficient and band structure of layered phononic crystals, the relationship between the transmission coefficient of layered phononic crystals and the number of layers, the thickness of layers, the sequence and the wavelength is revealed, and the band gap range of the two-component double-layer single cell phononic crystal material is proved. It is theoretically proved that when the thickness of single cell is given, increasing the number of layers will increase the attenuation effect first and then decrease it; when the materials of each layer are given, the inversion of sequence will not affect the transmission coefficient, and the combination of materials with large impedance difference can achieve better attenuation effect on most of frequencies. Based on the theoretical solution of the band structure of the layered phononic crystal, the band gap range of the phononic crystal with double-layer cells when the material is given is revealed. It is proved that the condition of realizing the maximum relative band gap width is when the volume ratio is equal to the wave speed ratio.A new method for inverse design of acoustic artificial materials based on supervised learning and reinforcement learning is developed, which can maximize the band gap width and realize the specified band gap range of acoustic metamaterials and layered phononic crystals. Based on supervised learning, the inverse design of acoustic metamaterials with two-dimensional circular inclusions is realized, which shows the feasibility of using parameters as inputs of neural network and has the advantages of reducing data scale and using previous knowledge. The high-precision prediction of band gap is realized, and the fast inverse design of band gap is realized by traversing the neural network. By applying reinforcement learning method on layered phononic crystals, the design of maximizing the first-order band gap width and the inverse design of specified band gap range is realized. The characteristics of evolution path are analyzed, and the high efficiency of reinforcement learning is proved. The interactive framework of reinforcement learning and mechanical simulation can be easily used in other mechanical design problems.