Estimation of Wave Reflection Coefficient by Semi-Analytical Method in an Acoustic Black Hole Beam

Abstract

Acoustic Black Hole (ABH) has been deployed into beam-plate structures with the passive damping system to enhance its performance in absorbing flexural waves. The wave reflection coefficient can be used to measure this performance. This paper proposes a semi-analytical method to estimate the wave reflection coefficient, which is based on the Finite Element Method (FEM). The proposed method is validated by the exact solution for the wave analysis on the quadratic ABH beam. By this method, this study also investigates the performances of power-law ABH beams with exponent [Formula: see text] and 10. The numerical results indicate that the wave reflection coefficient of ABH shows a decreasing trend as frequency increases. Moreover, the validity condition of the geometrical acoustic approach (GAA) is explored through error analysis on the estimated wave reflection coefficient. An envelope of this condition is presented to recommend conservative criteria for GAA.