Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype

Abstract

Periodic networks on the verge of mechanical instability, called Maxwell lattices, are known to exhibit zero-frequency modes localized to their boundaries. Topologically polarized Maxwell lattices, in particular, focus these zero modes to one of their boundaries in a manner that is protected against disorder by the reciprocal-space topology of the lattice's band structure. Here, we introduce a class of mechanical bilayers as a model system for designing topologically protected edge modes that couple in-plane dilational and shearing modes to out-of-plane flexural modes, a paradigm that we refer to as omnimodal polarization. While these structures exhibit a high-dimensional design space that makes it difficult to predict the topological polarization of generic geometries, we are able to identify a family of mirror-symmetric bilayers that inherit the in-plane modal localization of their constitutive monolayers whose topological polarization can be determined analytically. Importantly, the coupling between the layers results in the emergence of omnimodal polarization, whereby in-plane and out-of-plane edge modes localize on the same edge. We demonstrate these theoretical results by fabricating a mirror-symmetric, topologically polarized kagome bilayer consisting of a network of elastic beams via additive manufacturing and confirm this finite-frequency polarization via finite element analysis and laser-vibrometry experiments.

References in corpus (34)

• Topological Insulators
• Topological insulators and superconductors
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Topological Boundary Modes in Isostatic Lattices
• Topological mechanics of gyroscopic metamaterials
• Topologically protected elastic waves in phononic metamaterials
• Topological modes bound to dislocations in mechanical metamaterials
• Topological phonon modes and their role in dynamic instability of microtubules
• Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect
• Nonlinear conduction via solitons in a topological mechanical insulator
• Observation of topological valley modes in an elastic hexagonal lattice
• Selective buckling via states of self-stress in topological metamaterials
• Topological mechanics of origami and kirigami
• Transformable topological mechanical metamaterials
• Subwavelength and directional control of flexural waves in zone-folding induced topological plates
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Coriolis Force Induced Quantum Hall Effect for Phonons
• Topological phonons and Weyl lines in 3 dimensions
• Valley based splitting of topologically protected helical waves in elastic plates
• Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
• Topological edge floppy modes in disordered fiber networks
• Fracturing of topological Maxwell lattices
• Elasticity of Filamentous Kagome Lattice
• Valley-Hall In-Plane Edge States as Building Blocks for Elastodynamic Logic Circuits
• Effective Medium Theory of Filamentous Triangular Lattice
• Directional mechanical response in the bulk of topological metamaterials
• Universal Continuum Theory for Topological Edge Soft Modes
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• Hidden symmetries generate rigid folding mechanisms in periodic origami
• Kink-antikink asymmetry and impurity interactions in topological mechanical chains
• Mechanical Graphene
• Signatures of Topological Phonons in Superisostatic Lattices
• Topological Flexural Modes in Polarized Bilayer Lattices

Cited by in corpus (6)

• Non-Local Phononic Crystals for Dispersion Customization and Undulation-point Dynamics
• Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
• Robustness of stress focusing in soft lattices under topology-switching deformation
• Metamaterials and Fluid Flows
• Cell augmentation framework for topological lattices
• 3D Topologically Polarized Elastic Metamaterials Enable Asymmetric Energy Isolation at Low Frequencies