ZeroZero-energy topological oppy edge modes have been demonstrated in families of kagome lattices with geometriesthat differ from the regular case composed of equilateral triangles. In this work, we explore the behaviorof these systems in the limit of continuum elasticity, which is established when the ideal hinges that appearin the idealized models are replaced by ligaments capable of supporting bending deformation, as observed inrealistic physical lattices. Under these assumptions, the oppy edge modes are preserved but shifted to finitefrequencies, where they spectrally overlap with the acoustic bulk modes. The net result is the establishment ofa 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 withdifferent localization capabilities. Through theoretical analysis and finite element simulations, we parametricallyexplore the localization capabilities of different configurations, thus establishing a qualitative relation betweenthe topological descriptors of the unit cell and the effective global transmission properties of the lattice. Usingsimple elasticity arguments, we provide a mechanistic rationale for the observed range of behaviors. Our studyhas implications for the design of mechanical filters, structural logic components, and acoustic metamaterials forwave manipulation at large.
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