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.

Citation

Nieves, M. J., & Movchan, A. B. (2023). Asymptotic Theory of Generalised Rayleigh Beams and the Dynamic Coupling. . https://doi.org/10.1007/978-3-031-24141-3_11

• 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