Vibration damping by periodic additive acoustic black holes

Abstract

Embedded acoustic black holes (ABHs) have demonstrated significant efficiency in vibration mitigation. However, their practical application is limited due to their inherent low strength. To address this issue, this paper introduces an alternative approach of additive ABHs, which are periodically mounted on the host structure to simultaneously enhance structural rigidity and damping effects. The Gaussian expansion method (GEM) is employed to model the ABH beam and base beam within the framework of Timoshenko beam theory. The coupling between the two substructures is achieved using the nullspace method (NSM) based on the interface coupling condition. Additionally, the wave and Rayleigh–Ritz method (WRRM) is utilized to handle the Bloch-Floquet periodic boundary conditions. The complex dispersion curves are obtained using the k(ω) method, where the imaginary part represents the attenuating waves in space. The accuracy of the proposed model is validated against finite element simulations for the unit cell modes and dispersion curves. The results indicate that local resonance dominates the behavior, overshadowing the Bragg scattering effect. Furthermore, the inclusion of a damping layer results in a strong damping effect across a wide frequency band. Parametric studies reveal that larger lattice constant and increased uniform portion thickness of the ABH contribute to better damping performance, albeit with an associated increase in the added mass of the ABH component. Finally, the damping capability of finite periodic beams with 5 cells is investigated, assessing modal loss factor (MLF), transmissibility, and forced vibration shapes. The findings demonstrate that the proposed additive ABH approach opens up new possibilities for engineering applications.