To overcome the limitations of low computational efficiency and poor boundary adaptability of traditional acoustic black hole (ABH) calculation methods, this paper constructs a method for solving basis functions and develops an improved Rayleigh–Ritz method by combining the Galerkin expansion method, achieving rapid and accurate determination of the vibration characteristics of ABH beams. The accuracy and reliability of the proposed method are validated through numerical verification and comparisons with results from the literature. The study demonstrates that the results obtained using this method are in excellent agreement with reference data and numerical simulations. The first ten modal frequencies can be calculated in just 0.15 s, achieving a speed increase of more than two orders of magnitude compared to finite element models. In the analysis of complex geometric adaptability, the first ten modal frequencies show high consistency with finite element results, with a computational speed increase of approximately 111 times. A comparative analysis of the vibration responses of uniform beams, segmented ABH beams, and ideal ABH beams confirms that ABH structures exhibit significant vibration reduction capabilities over a wide frequency range. Optimal damping performance is achieved when the elastic modulus of the damping layer is in the range of Formula: see text and its density is between 950 and 1Formula: see text250Formula: see textkg/m 3 , while an excessive thickness of the damping layer is detrimental to performance enhancement. This study provides an efficient, reliable, and data-driven computational framework for the optimal design and engineering application of ABH structures.
Jiang et al. (Tue,) studied this question.