Isogeometric dynamic solution and energy transfer analysis of acoustic black hole beams

Acoustic black holes, as a commonly used and effective vibration reduction technique, require a precise structural dynamic modeling method. In this paper, the dynamic modeling method of an acoustic black hole beam with elastic boundary constraints is established by combining the isogeometric method and the energy formula. Firstly, based on the Euler-Bernoulli beam theory, the energy equations for uniform regions, ABH regions, and boundaries are derived. Then, the vibration control differential equations and power flow are obtained by using the geometric method and finite element ideal. Finally, the accuracy of the present solution for these beams is tested by comparing the ones with the numerical results obtained by COMSOL Multiphysics. Additionally, a systematic analysis of the dynamic response and energy distribution characteristics using the present method is presented. Numerical results show that the present method can accurately predict the aggregation effect of bending waves and vibration energy of an acoustic black hole beam with elastic constraint. The research provides a new analysis idea for the ABH design and effect analysis in these beams in engineering applications.