Dynamic characterization of a periodic microstructured flexural system with rotational inertia. (21st October 2019)

• Record Type: Journal Article
• Authors: Nieves, M. J.; Brun, M.
• Is Part Of: Philosophical transactions. Volume 377:Number 2156(2019)
• Publication Date: 2019-10-21
• Subjects: microstructured medium -- dispersion relation -- flexural waves -- Rayleigh beams; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rsta.2019.0113
• Languages: English
• ISSNs: 1364-503X

Abstract

Abstract : We consider the propagation of waves in a flexural medium composed of massless beams joining a periodic array of elements, elastically supported and possessing mass and rotational inertia. The dispersion properties of the system are determined and the influence and interplay between the dynamic parameters on the structure of the pass and stop bands are analysed in detail. We highlight the existence of three special dynamic regimes corresponding to a low stiffness in the supports and/or low rotational inertia of the masses; to a high stiffness and/or high rotational inertia regime; and to a transition one where dispersion degeneracies are encountered. In the low-frequency regime, a rigorous asymptotic analysis shows that the structure approximates a continuous Rayleigh beam on an elastic foundation. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.