Asymptotic Theory of Generalised Rayleigh Beams and the Dynamic Coupling

Nieves, Michael J.; Movchan, Alexander B.

Abstract

We consider the effective dynamic response of an infinite asymmetric structure formed from a beam attached to a periodic array of resonators. The array couples the axial and flexural motions of the beam. We develop a point-wise description of the response of the system and demonstrate that when the separation of the resonators is small, the structure is approximated by the generalised Rayleigh beam: a beam attached to an elastic resonant layer that engages flexural-longitudinal wave coupling. The passage to the effective model utilises a dynamic homogenisation based on the method of meso-scale approximations, whose efficiency is not limited to the typical low-frequency regime of usual homogenisation approaches. The dispersion properties of this effective system are completely characterised and we illustrate the multi-coupling of waves through the analysis of Green’s matrix of this flexural system, which is constructed in the explicit form. The analytical results are also accompanied by illustrative numerical computations.

• Start Date: Apr 12, 2023
• Acceptance Date: Apr 12, 2023
• Online Publication Date: Apr 12, 2023
• Publication Date: 2023
• Deposit Date: Jun 5, 2023
• Pages: 173-200
• ISBN: 9783031241406; 9783031241413
• DOI: https://doi.org/10.1007/978-3-031-24141-3_11
• Additional Information: First Online: 12 April 2023