摘要：The propagation characteristics of flexural waves in periodic grid structures designed with the idea of phononic crystals are investigated by combining the Bloch theorem with the finite element method. This combined analysis yields phase constant surfaces, which predict the location and the extension of band gaps, as well as the directions and the regions of wave propagation at assigned frequencies. The predictions are validated by computation and experimental analysis of the harmonic responses of a finite structure with 11 × 11 unit cells. The flexural wave is localized at the point of excitation in band gaps, while the directional behaviour occurs at particular frequencies in pass bands. These studies provide guidelines to designing periodic structures for vibration attenuation.

摘要：Higher-order topological insulators(HOTIs),with topological corner or hinge states,have emerged as a thriving topic in the field of topological ***,few connections have been found for HOTIs with well-explored first-order topological *** a proposal asserted that a significant bridge can be established between the HOTIs and Z2 topological *** subjected to an inplane Zeeman field,corner states,the signature of the HOTIs,can be induced in a Z2 topological *** Zeeman fields can be produced,for example,by the ferromagnetic proximity effect or magnetic atom doping,which drastically increases the experimental ***,we show that a phononic crystal,designed as a bilayer of coupled acoustic cavities,exactly hosts the Kane-Mele model with built-in in-plane Zeeman *** helical edge states along the zigzag edges are gapped,and the corner states,localized spatially at the corners of the samples,appear in the *** verifies the Zeeman field induced higher-order *** further demonstrate the intriguing contrast properties of the corner states at the outer and inner corners in a hexagonal ring-shaped sample.