Numerical study on shape functions for optimal exploitation of the acoustic black hole effect

• Published in: Proceedings in applied mathematics and mechanics 2021-01, Vol.20 (1), p.n/a
• Main Authors: Rothe, Sebastian, Dorn, Matthias, Langer, Sabine Christine
• Format: Article
• Language: English
• ISSN: 1617-7061; 1617-7061
• DOI: 10.1002/pamm.202000008

The acoustic black hole (ABH) effect offers a great possibility to damp a whole construction in a very efficient way. The main idea of this approach is to weaken thin structures locally to concentrate the structure‐borne sound energy in this area. Therefor material is removed in a certain region, which is referred to as an ABH. This measure leads to a focusing of acoustically critical bending waves. By applying a damping measure, e.g. constraint‐layer damping, within the ABH, the structure is globally damped by a local measure. The shape function of an ABH is a major issue for optimizing the efficiency of damping. The material diminution, equivalent to the reduction of the mechanical impedance, has to be smooth in order to avoid reflection of bending waves. In literature, a power function with a higher order than two is recommended. Focusing the structure‐borne sound works better by increasing the order. The limit case is infinite order which is a sharp step transition. This is equivalent to an impedance step which is well known to lead to a high portion of reflection and therefor reducing the efficiency of the ABH area. There must be an optimum between these two limits, quadratic and infinite order, in an acoustical sense. In this paper, numerical studies are carried out to determine the optimal order for a power function approach as shape function of an ABH. For this purpose, a beam is used as a generic structure. In addition, alternative function approaches are investigated and compared.