Vibrations and elastic waves in chiral multi-structures
arXiv:1805.01170 · doi:10.1016/j.jmps.2018.07.020
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.
arXiv comment31 pages, 11 figures
References in corpus (10)
- Observation of phononic helical edge states in a mechanical 'topological insulator'
- Topological Phononic Crystals with One-Way Elastic Edge Waves
- Topological mechanics of gyroscopic metamaterials
- Tilted resonators in a triangular elastic lattice: chirality, Bloch waves and negative refraction
- Vortex-type elastic structured media and dynamic shielding
- Interfacial waveforms in chiral lattices with gyroscopic spinners
- Transition wave in a supported heavy beam
- Quasi-periodicity and multi-scale resonators for the reduction of seismic vibrations in fluid-solid systems
- Edge waves and localisation in lattices containing tilted resonators
- Dispersion and localization in structured Rayleigh beams
Cited by in corpus (8)
- Configurational forces and nonlinear structural dynamics
- An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces
- Wave polarisation and dynamic degeneracy in a chiral elastic lattice
- Omnidirectional flexural invisibility of multiple interacting voids in vibrating elastic plates
- Nested Bloch waves in elastic structures with configurational forces
- Edge Waves and Transmissions for Temporal Laminates and Imperfect Chiral Interfaces
- Dispersion relations of generalized one-dimensional phononic crystals
- Dynamic Green's functions in discrete flexural systems