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Abstract Acoustic Black Holes (ABH) can concentrate and capture the energy of waves in specific regions of a structure. They offer significant advantages and application potential in manipulating bending waves and reducing vibrations and noise in thin-walled structures. This paper focuses on the ABH beam structure, employing a semi-analytical method to analyze its vibration characteristics. Firstly, an improved triangular series is used as the displacement-permitting function for the ABH beam. Based on the Ritz method, a semi-analytical model for the ABH beam is established. The modal analysis of the ABH beam is solved, showing good agreement with numerical results, and validating the reliability of the semi-analytical method. Subsequently, the forced vibration response of the ABH beam is studied in comparison to a homogeneous beam. The bandgap characteristics and vibration-damping properties of the ABH beam are analyzed. The results indicate that the ABH beam has multiple vibration suppression bandgaps compared to a homogeneous beam, and after applying damping to the ABH beam, it exhibits a certain level of vibration suppression effect.
Li et al. (Thu,) studied this question.