Tailoring low-frequency complete flexural bandgap with rotation-stiffening meta-plate

In this study, a two-dimensional rotation-stiffening meta-plate is proposed to realize a complete flexural bandgap that can be tailored to desired frequency ranges, including a broad range at low frequencies. Previously approaches to realize flexural bandgaps at targeted frequencies have predominantly relied on local resonances in unit cells or on band separation through decoupling of vertical and rotational motions. However, these approaches suffer from physical limitations: resonant designs typically exhibit narrowband behavior, and band separation through mode decoupling has been achieved only in one-dimensional systems. Here, we extend the concept of band separation through mode decoupling to a two-dimensional system by establishing a 2D meta-plate model formulated as a discrete analog based on the Mindlin-Reissner plate theory. Our analysis indicates that although a square-lattice 2D meta-plate can exhibit decoupled modes at band-edge states, mode degeneracy along the diagonal direction impedes the formation of a complete bandgap at low frequencies. From this key observation, we propose a novel strategy called “rotation-stiffening,” which enables the opening of a complete bandgap even in the presence of degeneracy. Building upon this concept, we designed a continuum meta-plate in which spherical masses are interconnected by pairs of slender beams, effectively constraining rotational motion. Numerical simulations and experiments were conducted to evaluate the vibration transmission characteristics over all in-plane directions, confirming the complete bandgap performance. These findings establish a systematic tailoring strategy for realizing low-frequency complete flexural bandgaps in two-dimensional plates and provide a promising approach for effective vibration mitigation through flexural-wave attenuation.