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A Simplified Modeling Framework of Higher-Order Topological States in Elastic Metaplates

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Abstract

Higher-order topological insulators (HOTIs) extend beyond conventional topological materials by supporting higher-dimensional topological corner/hinge states, offering unprecedented opportunities for wave control in elastic systems. While phononic crystals composed of thin plates loaded by prisms/pillars have demonstrated HOTI phenomena, the intricate polarization properties of elastic waves complicate theoretical modeling and predictive design. Herein, a simplified elastic metaplate composed of periodically arranged plate-pillar clusters (PPCs), achieving higher-order corner states through the integration of dual PPCs with inverted topological phase properties, is proposed. Furthermore, a theoretical framework for PPC metaplates using a "mass-spring" model in conjunction with multiple scattering theory is developed. The feasibility of the theoretical results is validated through simulations and experiments, successfully enabling theoretical modeling of higher-order topological corner states in elastic wave systems. The design strategy and findings presented in this article provide important design references for the development of high-dimensional, robust topological waveguides and devices in elastic wave systems.