Enhanced absorption with multiple quadratically tapered elastic wedges of different lengths terminating a uniform beam

Abstract

Tapered elastic wedges can be used to control flexural vibrations and this article explores a method of enhancing the performance of such terminations using multiple wedges. A system design where a uniform beam is terminated by multiple quadratically tapered wedges of different lengths is proposed, aiming to enhance the absorption of flexural vibrations. An analytical method based on the exact solution of the non-uniform one-dimensional Euler–Bernoulli beam is used to analyse this system, with the additional assumptions that the moments and forces at the junction from the side of the beam are balanced by the sums of the moments and forces of the wedges. The analytical model is compared with Finite Element simulations and its range of validity is discussed. Differences arise between the analytical and numerical results due to torsional effects, however, it is shown that a trident-shaped configuration can be used to suppress the effect of torsion. Simulations using the analytical model show that for the proposed multiple-wedge termination, more frequency bands of very low reflection, and thus very high absorption, appear compared to single-wedge terminations. Such bands of low reflection also occur at lower frequencies, where the absorptive capability of a single wedge is limited. An analysis of the zeros of the reflection coefficient in the complex-frequency plane is used to investigate the enhanced absorption through the concept of critical coupling. This analysis shows that the multiple-wedge termination leads to richer modal content due to the modal coupling between the wedges of different lengths, and that for appropriate length combinations very little damping can give very high absorption at certain frequencies. The proposed design thus provides significant enhancement of absorptive behaviour compared to a single-wedge termination.

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Identifiers

ORCID for Kristian Hook: orcid.org/0000-0002-5011-0414

ORCID for Jordan Cheer: orcid.org/0000-0002-0552-5506

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