Acoustic black holes (ABH) are a promising measure for improving the vibration behaviour of lightweight structures. Their potential can be further exploited through additive manufacturing (AM), which allows for greater design freedom and multi-material designs compared to conventional processes. In order to fully exploit the potential of AM for ABH structures, a clear understanding of the interactions between process parameters, geometric parameters, mechanical variables and vibration behaviour is required. Global sensitivity analyses (GSA) combined with ABH models enable the precise identification and quantification of these fundamental relationships. However, sample-based GSA approaches require a large number of model evaluations, which leads to very high computational costs when numerical methods such as the finite element method (FEM) are used. This contribution therefore presents a semi-analytical 1D ABH model based on Timoshenko's beam theory, which enables efficient and comprehensive global sensitivity analyses. The ABH area is divided into discrete beam elements with effective geometric and material-specific properties due to the multi-material design. Numerical validation of the model using FEM shows that the vibration behaviour can be predicted with sufficient accuracy over a wide frequency range. Based on this, a global sensitivity analysis was also carried out to determine the influence of geometric parameters on the vibration behaviour, revealing largely non-additive, clearly non-linear behaviour with pronounced interaction effects. In summary the proposed modelling approach offers considerable potential for further investigation of various fundamental relationships between additively manufactured ABH structures and vibration properties compared to numerical methods.
Heck et al. (Thu,) studied this question.