The Benefit of a Multi-wedge Acoustic Black Hole at Low-frequency Mitigation

Abstract

Introduction Acoustic black holes (ABH) are capable to mitigate structural vibrations efficiently above a certain cut-on frequency. The most commonly used geometry for a flexible beam is a simple wedge following a power-law curve. A simple wedge demands large dimensions for achieving mitigation in the low-frequency range below 1000 Hz. It was shown recently by experiments and numerical simulation that a multi-wedge configuration is beneficial for realizing a compact design and still showing good performance at low frequencies. Materials and Methods The WKB approximation is extended for a single-wedge design. Expressions for the reflection coefficient and cut-on frequency are discussed for an arbitrary number of wedges—the suggested multi-wedge ABH. Results The main benefit of the stacked multi-wedge ABH is a great improvement in performance in the low-frequency range. A numerical example highlights the successful vibration mitigation. It is shown how a multi-wedge ABH is tuned towards low-frequency in terms of cut-on frequency and reflections’ coefficient. The improved performance of a multi-wedge ABH is benchmarked against the well-established simple ABH.