Abstract
We develop a new asymptotic model of the dynamic interaction between an elastic structure and a system of gyroscopic spinners that make the overall multi-structure chiral. An important result is the derivation and analysis of effective chiral boundary conditions describing the interaction between an elastic beam and a gyroscopic spinner. These conditions are applied to the analysis of waves in systems of beams connected by gyroscopic spinners. A new asymptotic and physical interpretation of the notion of a Rayleigh gyrobeam is also presented. The theoretical findings are accompanied by illustrative numerical examples and simulations.
Highlights
Chirality, the property of an object whereby it is not congruent to its mirror image, occurs both through natural and man-made means in various areas of science
The present paper utilises an asymptotic analysis to develop a new type of chiral boundary conditions and a subsequent study of a class of spectral problems for chiral elastic multi-structures
A new class of chiral boundary conditions has been derived and analysed for elastic multi-structures incorporating elastic beams connected to gyroscopic spinners
Summary
The property of an object whereby it is not congruent to its mirror image, occurs both through natural and man-made means in various areas of science. Chirality may be introduced by gyroscopic spinners connected to a multi-structure, which may incorporate several elastic components. The present paper utilises an asymptotic analysis to develop a new type of chiral boundary conditions and a subsequent study of a class of spectral problems for chiral elastic multi-structures. A new class of chiral boundary conditions has been introduced in Carta et al (2018) for a gyro-hinge connecting a gyroscopic spinner and an elastic beam. Chirality can yield counter-intuitive behaviour in the static response of a material Examples of this include Prall and Lakes (1997), where honeycomb structures composed of rigid rings linked by slender ligaments were modelled and experimentally analysed.
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