Zero-frequency corner modes in mechanical graphene
arXiv:2212.06960 · doi:10.1016/j.wavemoti.2024.103291
Abstract
In an unconstrained elastic body, emergence of zero natural frequencies is an expectable outcome on account of the body's ability to purely translate or rotate with no structural deformation. Recent advances in literature have pushed such conventional definition and demonstrated properties transcending typical zero-frequency modes, such as localization of deformation at a structural edge or corner. In this paper, a spring-mass honeycomb lattice with an elastic foundation, referred to here as mechanical graphene, is designed to exhibit zero-frequency corner modes. A central element in the proposed design is the elastic foundation, and the zero-frequency corner modes are enabled by intricate modulation of the elastic-foundation's stiffness. These modes are proven to have their origins from the dynamics of a diatomic chain, made from a single strip of the mechanical graphene with free boundaries. Different shapes of finite mechanical graphene with free boundaries are considered and conditions leading to the manifestation of corner modes are correlated with the angle of corners and stiffness of springs supporting them. Finally, the effect of defects on zero-frequency corner modes is briefly discussed, demonstrating robustness against structural defects that are distant from corners.
References in corpus (17)
- Observation of phononic helical edge states in a mechanical 'topological insulator'
- Observation of a phononic quadrupole topological insulator
- Topological Boundary Modes in Isostatic Lattices
- Topological mechanics of gyroscopic metamaterials
- Elastic higher-order topological insulator with topologically protected corner states
- A fractional corner anomaly reveals higher-order topology
- Topological Phase Transition in Mechanical Honeycomb Lattice
- Manipulation of Dirac Cones in Mechanical Graphene
- Formation of Local Resonance Band Gaps in Finite Acoustic Metamaterials: A Closed-form Transfer Function Model
- Topological edge floppy modes in disordered fiber networks
- Mechanical Graphene
- Theory of Truncation Resonances in Continuum Rod-based Phononic Crystals with Generally Asymmetric Unit Cells
- Closed-form existence conditions for band-gap resonances in a finite periodic chain under general boundary conditions
- Existence of Corner Modes in Elastic Twisted Kagome Lattices
- Uncertainty Quantification of Tunable Elastic Metamaterials using Polynomial Chaos
- Controlling the Deformation of Metamaterials: Corner Modes via Topology
- Designing topological acoustic lattices via electroacoustic analogies