Broadband traveling wave generation using acoustic black holes

TL;DR

This work demonstrates that acoustic black holes (ABHs) can passively sustain broadband traveling waves in a finite beam when excited at a single point. A mixed Euler-Bernoulli beam model with a tapered ABH termination and a partial viscoelastic damping layer is developed and discretized via Galerkin methods, yielding a solvable framework with harmonic forcing. The model is validated against experiments on an aluminum ABH beam across 1 kHz–10 kHz and is then used in a parametric study to quantify how the viscoelastic loss factor, ABH power-law order, and ABH length influence traveling-wave content. The findings provide design guidance for ABH-based broadband TW generation, showing that with $m \approx 3$ and partial damping coverage, traveling-wave dominance ($CF \le 0.2$) can be achieved over a wide frequency range, enabling BM-inspired biomechanical modeling and broadband vibration control applications.

Abstract

This work studies the effectiveness of acoustic black holes to generate broadband non-reflective traveling waves using a single excitation source. This is inspired by similar observations in the basilar membrane of the mammalian inner ear. An aluminum beam is machined to introduce a gradual, asymmetric power-law taper at one of its ends. This tapered termination was then partially covered by viscoelastic tape to enhance the acoustic black hole effect in the system. This setup is then used to validate a model developed based on the Euler-Bernoulli beam theory. Following good agreement between the model and the experimental setup over a broad excitation frequency range (1 kHz to 10 kHz), the model is used to conduct a parametric study investigating the effects of different variables on the system's response. This study revealed the effectiveness of acoustic black holes in sustaining traveling waves over a broad frequency range. By optimizing parameters, such as the power-law order, one can significantly enhance this effect. This is especially noticeable towards the lower-frequency end.

Figures (14)

• Figure 1: Beam with ABH termination and viscoelastic damping layer.
• Figure 2: Experimental setup for viscoelastic damping characterization: (a) Oberst beam specimen with VEM layer, root section, and clamp; (b) dynamic testing with laser vibrometer and automatic modal hammer.
• Figure 3: FRFs of the bare and Oberst beams measured at the free end, showing the effect of the damping layer on the resonance amplitude, frequency shift, and bandwidth.
• Figure 4: Frequency-dependent storage modulus and loss factor of the damping material, extracted from FRFs using ASTM E756-05.
• Figure 5: Free-free beam with an ABH, integrated with piezoelectric patches and a viscoelastic damping layer.