The field of topological states of matter has garnered considerable attention across electronic, photonic, and phononic systems due to its remarkable abilities in waveguiding and localization, which remain robust against disorders and defects. A fundamental challenge in material physics lies in understanding the interplay between intrinsic properties and those induced by boundaries. In infinite periodic materials, resonant modes are notably absent within band gaps. However, when the material is truncated to form a finite periodic structure, these modes may appear as localized edge modes within the band gap. In this study, we introduce a generalized system by incorporating nonlocal interactions into the well-established Su-Schrieffer-Heeger (SSH) model. This generalized system exhibits a broader range of topological properties, including non-trivial topological phases and associated localized edge states. We conduct a detailed investigation of the zero-energy edge states, exploring their characteristics and behavior. Additionally, we discuss the influence of boundaries on the existence of edge states and consider the impact of Fifth Nearest Neighbors (FNNs) within the system.
Acoustoelastic metamaterials are widely used as composite cores in sandwich beams. However, discussions on the application of metamaterials in face sheets have been sporadic. In this work, we parametrically explore the dynamic behaviors of sandwich beams with metamaterials as face sheets. In addition to the capability of phonon dispersion modulation using periodic face sheets, the relative positions of top and bottom face sheets can further break their spatial symmetry and thus opens more bandgaps that are not achievable with one-dimensional periodic beams. Our study has implications for the design of sandwich beams to mitigate damages induced by vibrations in various engineering and industrial applications
Zero-energy topological oppy edge modes have been demonstrated in families of kagome lattices with geometries that differ from the regular case composed of equilateral triangles. In this work, we explore the behavior of these systems in the limit of continuum elasticity, which is established when the ideal hinges that appear in the idealized models are replaced by ligaments capable of supporting bending deformation, as observed in realistic physical lattices. Under these assumptions, the oppy edge modes are preserved but shifted to finite frequencies, where they spectrally overlap with the acoustic bulk modes. The net result is the establishment of a relatively broad low-frequency regime over which the lattices display strong asymmetric wave transport capabilities. By simply varying the thickness of the ligament of the unit cell, we can obtain a variety of lattices with different localization capabilities. Through theoretical analysis and finite element simulations, we parametrically explore the localization capabilities of different configurations, thus establishing a qualitative relation between the topological descriptors of the unit cell and the effective global transmission properties of the lattice. Using simple elasticity arguments, we provide a mechanistic rationale for the observed range of behaviors. Our study has implications for the design of mechanical filters, structural logic components, and acoustic metamaterials for wave manipulation at large.
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