基于高斯展开法的碟形声学黑洞半解析建模与宽频调谐减振机理研究

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摘要近年来，嵌入式声学黑洞（ABH）以其优异的性能，在结构减振降噪、声波调控、能量回收等领域展示了广阔的应用前景，但其局部结构强度弱化会影响其工程实用性。本文提出一种碟形声学黑洞(Dish-shaped acoustic black hole，DABH)结构，将其附加在主体结构上，以实现对主体结构的宽频减振。在Rayleigh-Ritz法框架下，选择高斯函数作为基函数，根据声学黑洞板的形状确定基函数的分布，避免质量和刚度矩阵的奇异化，建立了其耦合系统半解析模型。通过与有限元模态分析结果的对比，验证了半解析建模方法的正确性。研究了碟形声学黑洞结构参数以及连接位置对主体结构振动响应特性的影响规律，分析了碟形声学黑洞的ABH效应以及与主体结构的耦合效应，揭示了其宽频调谐减振的机理，为拓展声学黑洞在宽频结构振动控制上的应用提供了新的思路。

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	丁媛
	施凯耀
	郑玲

关键词 ：声学黑洞, 减振, 高斯展开法, DVA效应

Abstract：In recent years, embedded acoustic black holes (ABH) have shown extremely broad application prospects in the fields of structural vibration and noise reduction, sound wave control, and energy recovery with their excellent performance. However, the weakening of local structural strength will affect their engineering practicability. In this paper, a dish-shaped acoustic black hole (DABH) structure is proposed and attached to the main structure to achieve broadband vibration suppression of the main structure. Under the framework of Rayleigh-Ritz method, a gaussian function is selected as the basis function, the distribution of the gaussian function is determined according to the shape of the dish-shaped acoustic black hole, the singularization of the mass matrix and the stiffness matrix is avoided, and the semi-analytical analysis model of the coupling system is established. By comparing with the finite element modal analysis results, the correctness of the semi-analytical modeling method is verified. The influence of the structural parameters of the dish-shape acoustic black hole (DABH) and the connection position on the vibration response characteristics of the main structure are investigated. The ABH effect and the coupling effect with the main structure are analyzed, and the mechanism of broadband tuning and vibration are revealed. It demonstrates the application of ABH in broadband vibration control.

Key words： acoustic black holes vibration control Gaussian expansion dynamic vibration absorber effect

收稿日期: 2023-01-09 出版日期: 2024-01-28

引用本文:

丁媛，施凯耀，郑玲. 基于高斯展开法的碟形声学黑洞半解析建模与宽频调谐减振机理研究[J]. 振动与冲击, 2024, 43(2): 291-298.
DING Yuan， SHI Kaiyao， ZHENG Ling. Semi-analytical modelling of a dish-shaped acoustic black hole coupling system based on the Gaussianexpansion method and research on the vibration damping mechanism of broadband tuning. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(2): 291-298.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2024/V43/I2/291

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