Broadband vibroacoustic reduction for a circular beam coupled with a curved acoustic black hole via nullspace method

Add-on acoustic black holes (ABHs) tend to be popular in recent years because it is not mandatory to diminish the thickness of the host structure. Instead, ABHs are treated as vibration absorbers when they are mounted on the main body. This paper aims to mitigate the vibroacoustic issues of circular beams extensively employed in aeronautics, among others. To this end, we propose a curved ABH design that is suitable to be mounted on the inner wall of a cylindrical shell. Based on the component modes computed with our previously established Gaussian expansion method (GEM), an exact nullspace method (NSM) is proposed to account for the coupling between the components at the interface. The NSM is validated via finite element simulations. Benefitting from the NSM, the modal coupling strength between the component modes is quantified, and it is revealed that it is strong at low frequencies but becomes weaker at high ones. After that, broadband vibration reduction capabilities of the curved ABH are characterized, thanks to the combined mechanism of the ABH effect and the added mass. For this reason, the radiated sound power is also significantly reduced. Finally, non-negative intensity is utilized to identify the active area responsible for the sound power. Results show that special attention must be paid to the coupling point and the excitation location.