二维SSH声子晶体中高阶拓扑模式的预测性梁-晶格约化模型
Predictive beam-lattice reduction for higher-order topological modes in a 2D SSH phononic crystal
浏览论文内容
中文总结 AI 辅助
本文提出一种力学忠实的二维SSH声子晶体约化模型，通过欧拉-伯努利梁理论推导12自由度厄米动力学矩阵，利用该模型预测并验证了拓扑带隙内的边界与角模式，为设计拓扑弹性超材料提供了新途径。
中文摘要 AI 辅助
我们开发了一种力学上忠实的约化模型，用于研究由刚性方形质量块通过细长弹性韧带连接构成的二维拓扑声子晶体。利用欧拉-伯努利梁理论，我们推导了一个具有12个自由度的厄米动力学矩阵，该矩阵保留了面内平移、旋转以及韧带偏心的特性。这种约化模型捕捉到了标量质量弹簧SSH模型所缺失的效应，同时相比完整的有限元模拟，其计算效率高得多且更易于解释。通过使韧带宽度二聚化，可得到具有完整带隙和量化体极化的二维SSH力学晶格。二聚化的符号控制着从平庸相到非平庸相的转变，而韧带偏心则提供了一种额外的纯几何机制来改变拓扑性质。能带和有限元计算预测了带隙内的边界模式和角模式，这些模式通过局域化度量进行量化，并通过有限元模拟得到验证。对3D打印样品的测量显示，平庸结构呈现消逝响应，而非平庸结构在预测的带隙内表现出增强的边界/角响应。研究结果提供了一条经过验证的途径，可用于设计拓扑弹性超材料，采用的是连续介质启发的离散模型，而非理想化的质量弹簧网络或蛮力数值优化方法。
英文摘要
We develop a mechanically faithful reduced model for a two-dimensional topological phononic crystal composed of rigid square masses connected by slender elastic ligaments. Exploiting Euler Bernoulli beam theory, we derive a Hermitian 12 degree of freedom dynamical matrix that retains in-plane translations, rotations, and ligament eccentricity. This reduction captures effects that are absent from scalar mass spring SSH models while remaining computationally much more tractable and more easily interpretable than full finite element simulations. Dimerizing the ligament widths produces a mechanical 2D SSH lattice with a full band gap and a quantized bulk polarization. The sign of the dimerization controls the transition from trivial to non trivial phases, while ligament eccentricity provides an additional purely geometric mechanism for changing the topology. Ribbon and finite cell calculations predict in gap edge and corner modes, quantified by localization measures and confirmed by finite element simulations. Measurements on 3D printed samples show an evanescent response in the trivial structure and enhanced boundary/corner response in the non trivial structure within the predicted gap. The results provide a validated route for designing topological elastic metamaterials using a continuum informed discrete model rather than either idealized mass spring networks or brute force numerical optimization.
