Local-Resonance-Induced Dual-Band Topological Corner States of Flexural Waves in a Perforated Metaplate

Abstract

Despite their proven effectiveness in localizing and steering subwavelength elastic waves, locally resonant elastic topological insulators (TIs) with surface-mounted or embedded resonators are often challenged because of their structural complexity and the difficulty in realizing multiple topological band gaps. Here we present a second-order elastic TI (SETI), made of a perforated metaplate with a series of etched C-shaped slots, to achieve dual-band topological corner states. The etched slots in the metaplate form a type of cantileverlike oscillator, the multimodal bending resonances of which couple with the flexural vibration modes of the metaplate, resulting in multiple locally resonant band gaps. Judiciously configuring these slots in a ${C}_{4v}$-symmetric lattice enables topologically distinct metastructures and creates a SETI. We numerically and experimentally observe the dual-band corner states in two broad topological band gaps. Our platform for observing the topological effects in a perforated metaplate greatly simplifies the fabrication of metastructures for implementing locally resonant elastic TIs, benefiting applications of TIs at the subwavelength scale such as elastic wave trapping and energy amplification.