Vibration and power flow analysis of a uniform beam coupled with an ABH beam with arbitrary angles

This study establishes a model of a uniform beam coupled with an Acoustic Black Hole (ABH) beam, considering arbitrary connection angles. Translational and rotational springs are used to simulate the connection stiffnesses as well as the elastic boundary conditions. Under the general Rayleigh-Ritz framework, a modified Fourier series is chosen as the admissible function for the flexural and longitudinal displacements of the ABH coupled beam. The modified Fourier series ensures the continuity of higher-order spatial derivatives across the entire solution domain, enabling the calculation of structural intensity and power flow within the ABH coupled beam. Accurate predictions of the modal characteristics and dynamic response of the system are verified through comparisons with results simulated from FEM or experimental data. Subsequently, numerical examples are presented to study the ABH effect and vibration energy transmission in the coupled system. The excellent energy focalization characteristic is observed, and the unfavorable ABH failure phenomenon is also confirmed. Two mechanisms of ABH failure are revealed through power flow analysis: energy localization and coupling node hindering effects. Finally, the effect of coupling angle variation on vibrational energy transmission in the system is investigated. The established theoretical model and the phenomenon presented in this work provide guidance for applying ABH in coupled beam structures and promote its use in complex systems.