Damping of vibration in beams and plates using curved acoustic black holes with consideration of cut-on frequency

Abstract

This study aims at reducing the vibration in beams and plates using curved acoustic black holes (ABHs) whose baselines are curved to save the space occupied by the ABHs while maintaining the vibration-damping performance of straight ABHs. The exact solution of wave motion in straight ABHs with arbitrary exponents is derived and it is utilized to determine the cut-on frequency. In addition, the exact solution is used for analysis of the wave motion in an ABH supported by an impedance support. Then, the coupled differential equations of wave motion in curved ABHs are formulated and the cut-on frequencies are determined by solving them. It is shown that there is a trade-off relationship between a compact design and a low cut-on frequency. Furthermore, a spiral ABH-based waveguide absorber (WGA) is proposed to suppress the vibration in plates with light weight and compact space, and the damping performance is investigated experimentally by measuring the mobility of a fluid-filled box structure with optimized WGAs.