Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect
Damping of structural vibrations in beams and elliptical plates using the acoustic black hole effect
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DOI：
10.1016/j.jsv.2010.12.001
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发表时间：
2011-05-23
影响因子：
4.7
通讯作者：
Krylov, V. V.
中科院分区：
文献类型：
--
作者：
Georgiev, V. B.;Cuenca, J.;Krylov, V. V.
如果梁和板的厚度减小，弯曲波的传播速度就会减慢。这种性质在过去被用来建立声学黑洞（ABH）理论。本文的目的是建立可靠的数值和实验方法的设计，建模和制造一个有效的被动减振器使用ABH效应。这种振动吸收器的有效性随着频率而增加。首先，欧拉-伯努利梁的动态行为表示使用阻抗方法，这反过来又导致梁阻抗的Riccati方程。这个方程是使用自适应龙格-库塔-Fehlberg方法数值积分，产生的频率和空间依赖的阻抗矩阵的光束，从反射矩阵获得。此外，该数学模型可以扩展到包含吸收膜，该吸收膜有助于减少来自截断边缘的反射波。因此，吸收膜的几何和材料特性的影响进行了研究，并提出了这些参数的最佳配置。本文介绍了一个在椭圆板的一个焦点上放置一个幂律凹坑的实验。板的椭圆形形状诱导朝向ABH的波的完全聚焦，以防它们在另一焦点中产生。因此，导出的欧拉-伯努利梁的一维方法可以作为一种唯象模型，有助于更好地理解二维椭圆结构中的复杂过程。最后，数值模拟和实验测量都表明振动水平显着降低。(c)2010爱思唯尔有限公司保留所有权利。
Flexural waves in beams and plates slow down if their thickness decreases. Such property was used in the past for establishing the theory of acoustic black holes (ABH). The aim of the present paper is to establish reliable numerical and experimental approaches for designing, modelling and manufacturing an effective passive vibration damper using the ABH effect. The effectiveness of such vibration absorbers increases with frequency. Initially, the dynamic behaviour of an Euler-Bernoulli beam is expressed using the Impedance Method, which in turn leads to a Riccati equation for the beam impedance. This equation is numerically integrated using an adaptive Runge-Kutta-Fehlberg method, yielding the frequency- and spatially-dependent impedance matrix of the beam, from which the reflection matrix is obtained. Moreover, the mathematical model can be extended to incorporate an absorbing film that assists for reducing reflected waves from the truncated edge. Therefore, the influence of the geometrical and material characteristics of the absorbing film is then studied and an optimal configuration of these parameters is proposed. An experiment consisting of an elliptical plate with a pit of power-law profile placed in one of its foci is presented. The elliptical shape of the plate induces a complete focalisation of the waves towards ABH in case they are generated in the other focus. Consequently, the derived 1-D method for an Euler-Bernoulli beam can be used as a phenomenological model assisting for better understanding the complex processes in 2-D elliptical structure. Finally, both, numerical simulations and experimental measurements show significant reduction of vibration levels. (c) 2010 Elsevier Ltd. All rights reserved.