Topological edge states of quasiperiodic elastic metasurfaces
arXiv:2205.00531 · doi:10.1016/j.ymssp.2022.109478
Abstract
In this work, we investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces, namely arrays of mechanical oscillators arranged over the free surface of an elastic half-space according to a quasiperiodic spatial distribution. An ad-hoc multiple scattering formulation is developed to describe the dynamic interaction between Rayleigh waves and a generic array of surface resonators. The approach allows to calculate the spectrum of natural frequencies of the quasiperiodic metasurface which reveals a fractal distribution of the frequency gaps reminiscent of the Hofstadter butterfly. These gaps have nontrivial topological properties and can host Rayleigh-like edge modes. We demonstrate that such topologically protected edge modes can be driven from one boundary to the opposite of the array by a smooth variation of the phason, a parameter which modulates the geometry of the array. Topological elastic waveguides designed on these principles provide new opportunities in surface acoustic wave engineering for vibration control, energy harvesting, and lossless signal transport, among others.
References in corpus (21)
- Topological Photonics
- Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
- Topological Acoustics
- Acoustic topological insulator and robust one-way sound transport
- Topological States and Adiabatic Pumping in Quasicrystals
- Observation of topological valley transport of sound in sonic crystals
- Topological Phononic Crystals with One-Way Elastic Edge Waves
- Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
- Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
- Topological negative refraction of surface acoustic waves in a Weyl phononic crystal
- Seismic metasurfaces: Sub-wavelength resonators and Rayleigh wave interaction
- Edge states and topological pumping in elastic lattices with periodically modulated coupling
- Experimental observation of temporal pumping in electro-mechanical waveguides
- Observation of topological edge modes in a quasi-periodic acoustic waveguide
- Edge States and Topological Pumping in Stiffness Modulated Elastic Plates
- Surface wave non-reciprocity via time-modulated metamaterials
- Lamb's problem for a half-space coupled to a generic distribution of oscillators at the surface
- Adiabatic pumping via avoided crossings in stiffness modulated quasiperiodic beams
- Exploring Topology of 1D Quasiperiodic Metastructures through Modulated LEGO Resonators
- Dipolar localization of waves in twisted phononic crystal plates
- The K-Theoretic Bulk-Boundary Principle for Dynamically Patterned Resonators