基于高斯展开法的碟形声学黑洞宽频调谐减振机理研究

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

近年来,嵌入式声学黑洞(acoustic black holes,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。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。

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 owing to their excellent performance.However,the weakening of local structural strength will affect their engineering practicability.A dish-shaped acoustic black hole(DABH)structure was 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 was selected as the basis function.The distribution of the Gaussian function was determined according to the shape of the dish-shaped acoustic black hole in oder to avoid the singularization of the mass matrix and the stiffness matrix,and the semi-analytical analysis model of the coupling system was established.By comparing with the finite element modal analysis results,the correctness of the semi-analytical modeling method was verified.The influences of the structural parameters of the DABH and the connection position on the vibration response characteristics of the main structure were investigated.The ABH effect and the coupling effect with the main structure were analyzed,and the mechanism of broadband tuning and vibration reduction were revealed.The study provides a new way of thinking for the application of ABH in broadband vibration control.