Interface modes in topologically protected edge states using hourglass based metastructures

Abstract

This study reports the presence of an interface mode in the one-dimensional topologically arranged mechanical metamaterials using mechanical dome shaped metastructures which can be exhibited by hourglass configurations. The paper proposes the method of obtaining a localized interface mode within the bandgap using the hourglass shaped resonating elements in the one dimensional topologically arranged chain. Implementing a wide range of different re-entrant angles on the patterns imprinted on dome shaped hourglass metastructure ranging from negative to positive re-entrant angle would lead to lattice dependent stiffness characteristics in the system. The primary unit cell considered in this system is diatomic unit cell having identical masses and alternating spring stiffness driven by the dome shaped hourglass metastructure. Moreover, the variation in the stiffness of hourglass metastructure is also dependent on the height to thickness ratio which is also explored in this study to restrict the stiffness of hourglass unit in the linear regime which is easily obtainable in small deformation range. The interface unit cell is placed in the one-dimensional chain in such a way that inversion symmetry is broken using the different classes of hourglass lattice metastructures within the unit cell. The frequency response function of the one dimensional topologically protected chain is analytically computed and the interface mode is observed locally within the bandgap. The possibility of wave propagation at specific frequencies within the bandgaps is strategically achieved by defining lattice-dependent stiffness parameters at the interface modes. The considered configurations define a framework for introducing lattice-based imperfections in the continuous elastic structures that makes it potential engineering relevance.