Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators

Nieves, M.J.; Carta, G.

doi:10.1007/s10665-021-10110-w

Analytical treatment of the transient motion of inertial beams attached to coupling inertial resonators

Nieves, M.J.; Carta, G.

Authors

Michael Nieves m.nieves@keele.ac.uk

G. Carta

Abstract

This paper presents, for the first time, an analytical formulation to determine the transient response of an elastic beam possessing distributed inertia and connected to a coupling inertial resonator, represented by a gyroscopic spinner. The latter couples the transverse displacement components of the beam in the two perpendicular directions, thus producing roto-flexural vibrations. A detailed parametric study is presented that illustrates the effects of the beam’s distributed inertia and of the resonator’s characteristics. The limit case of massless beam is examined and it is shown that in some situations the distributed inertia in the beam should not be neglected. Analytical results are also validated by finite element computations. An illustration is also presented that demonstrates the effectiveness of using the considered inertial devices to mitigate hazardous vibrations in structural systems. It is envisaged that this paper may be useful in the analysis of flexural waveguides and metamaterials consisting of inertial elastic beam elements.

Journal Article Type	Article
Acceptance Date	Feb 13, 2021
Publication Date	Mar 20, 2021
Journal	Journal of Engineering Mathematics
Print ISSN	0022-0833
Publisher	Springer Verlag
Peer Reviewed	Peer Reviewed
Volume	127
Article Number	20
DOI	https://doi.org/10.1007/s10665-021-10110-w
Keywords	Flexural waves, Transient analysis, Inertial resonator, Gyroscopic spinner, Vibration isolation
Publisher URL	http://doi.org/10.1007/s10665-021-10110-w