Efficient prediction of the response of finite acoustic black hole structures under distributed loads

Abstract

This study presents an analytical approach for investigating the dynamic behaviour of finite Euler-Bernoulli beams with one or more embedded Acoustic Black Holes (ABHs) under distributed loading. The proposed approach is based on the Method of Varying Amplitudes, which enables the computation of natural frequencies and mode shapes for finite structures with thickness modulation. Notably, the approach is applicable to various structural geometries, including classical power-law profiles and harmonic profiles constituting periodic ABH-like structures. The natural frequencies and mode shapes of the beams with incorporated ABHs are used to calculate their response to external arbitrarily distributed loading. Case studies involving both concentrated and distributed loads are used to validate the accuracy and robustness of the proposed method, with results compared to numerical simulations. The approach offers valuable insights for the design and optimization of finite ABH structures for vibration suppression under arbitrarily distributed loading and applications in noise control.