基于周期性声学黑洞（ABH）板结构的中低频振动控制研究

The Acoustic Black Holes (ABH) effect is a new wave manipulation method, which reduces the phase velocity of flexural waves to zero when the structural thickness approaches zero according to a power-law thickness variation, resulting in zero wave reflections and high energy concentrations at the wedge tip. The ABH effect thus shows promising application potentials for vibration controls since only a very small amount of damping materials is required at the energy focalization region. However, systematic broadband ABH effects can only be achieved above a certain frequency when the incoming wavelength is comparable or smaller than the characteristic dimension of the ABH cell. This seriously impedes the application range of the ABH-based technology since the main and the most challenging difficulty is rather in the mid-to-low frequency range. Therefore, this project proposes to investigate periodic plates with ABH profiles to achieve effective vibration control in the mid-to-low frequency range by applying the ABH effect and the concept of Phononic Crystals. The theoretical semi-analytical model of periodic plates with ABH features is established to systematically reveal the wave propagation characteristics and potential band gaps and their physical mechanism. The effect of ABH structural parameters on band gaps is analyzed comprehensively, and the optimization model is further established to guide and design the ABH plate which not only meets the requirements of highly-efficient vibration control in mid-to-low frequency range, but also meets the requirements of practical engineering applications. This project will be of great academic significance and practical value to analyze and solve the vibration control problems in mid-to-low frequency range.

声学黑洞（简称ABH）效应是一种新兴的波操控方法，利用波在厚度逐渐减小结构中的传播特性可以达到理想情况下波的零反射，其产生的能量聚集效应可以实现非常有效的减振效果，因此在振动控制领域具有巨大的应用前景。然而，受ABH结构尺寸影响，现有ABH结构的有效控制频率主要集中在中高频，而中低频振动控制才是实际工程应用中的重点和难点。基于此，通过结合ABH机理和声子晶体的概念，本项目提出研究基于周期性声学黑洞板结构的中低频振动控制。通过建立周期性ABH板结构的理论半解析模型，系统揭示其结构内的波传播特性和潜在产生的带隙及其物理机理，全面分析ABH结构参数对带隙产生的影响规律，并进一步建立优化模型，指导和设计出既满足高性能的中低频减振效果，又满足实际工程应用强度要求的ABH板结构。本项目将对推动和指导中低频振动控制问题的分析和解决具有重要的学术意义和实用价值。

针对声学黑洞（ABH）结构受结构尺寸影响，有效作用频率主要集中在中高频的瓶颈问题，本项目通过结合声学黑洞效应和声子晶体的概念，提出了研究基于周期性声学黑洞板结构的中低频振动控制方法。通过分析ABH板结构中波的传播路径，设计出新型的周期性ABH一维和二维板结构，并建立了相应的分析模型，获得了包括中低频的宽频带隙，系统揭示了其结构内的波传播特性和带隙产生的物理机理，实现了中低频振动控制。同时，全面分析了ABH结构参数对带隙产生的影响规律，提出了高性能中低频减振效果的周期性ABH结构的设计准则，并实验验证了该类结构有效的减振隔振效果，有利于推动和指导中低频振动控制问题。此外，根据项目的进度和完成情况进行了适度的拓展与延伸，分析了周期性ABH板结构的声辐射特性，通过结合ABH效应和亚波长带隙，该类结构在超宽频率范围内能有效降低结构的声辐射。最后，本项目还在已有成果的基础上，开展了部分探索性研究。

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