Acoustic Black Holes in a Spinning Beam

Abstract

Through creating slow waves in structures, acoustic black hole (ABH) shows promise for potential vibration control applications. However, it remains unclear whether such phenomena can still occur in a structure undergoing high-speed spinning, and if so, what is the interplay among various system parameters and what are the underpinning physical mechanisms. To address this issue, this work establishes a semi-analytical model for a spinning ABH beam based on Euler–Bernoulli beam theory under the energy framework. After its validation, the model is used to reveal a few important vibration features pertinent to the spinning ABH beam through examining its dynamics, modal properties, and energy flow. It is shown that the spinning-induced centrifugal effects generate hardening effects inside the structure, thus increasing the overall structural stiffness and stretching the wavelength of the modal deformation of flexural waves as compared with its counterpart at rest. Meanwhile, energy flow to the ABH portion of the beam is also adversely affected. As a result, the ABH-induced overall damping enhancement effect of the viscoelastic coating, as observed in conventional ABH beam at rest, is impaired. Nevertheless, the study confirms that typical ABH features, in terms of wave compression, energy trapping, and dissipation, though affected by the spinning effects, are still persistent in a high-speed spinning structure. This provides the theoretical basis for the ABH phenomena in the design of high-performance rotating mechanical components such as turbine blades.