Power flow and structural intensity analyses of Acoustic Black Hole beams

Abstract

A truthful description of the energy transport process is vital for the understanding of the Acoustic Black Hole (ABH) effect and its applications. One of the parameters, which can depict such a physical process is the power flow, whose calculation involves higher-order derivatives of the structural displacement function. This however requires an accurate and sufficiently smooth fitting of the structural responses which can hardly be achieved by the existing semi-analytical models on ABH structures. To tackle the problem, an energy formulation, in conjunction with a Rayleigh-Ritz procedure, is proposed for an ABH beam, whose thickness variation is described as a general Fourier expansion. The transverse displacement of the beam is constructed using Fourier series with supplementary auxiliary functions. This treatment ensures the continuity and the smoothness of all relevant derivatives terms in the entire calculation domain, thus allowing the calculation of the power flow and structural intensity. Numerical examples are presented to illustrate the reliability and the effectiveness of the established model. Numerical analyses on power flow and structural intensity show the spatial and frequency characteristics of the energy transmission process and reveal the ABH-specific mechanisms. While providing an efficient analysis tool, this work enriches the existing understanding on the dynamic behavior of ABH structures.