标题： 高频参数近似方法在反四重旋材料的弗洛凯-布洛赫谱中的应用 显示英文标题

标题： High-frequency parametric approximation of the Floquet-Bloch spectrum for anti-tetrachiral materials

摘要： 由抗四重周期细胞材料构成的工程类别在现象上通过弹性宏观响应的强负泊松比特性来表征。 这种具有明显各向异性的负泊松效应是由刚性环和柔性连接件的周期性图案所发展的滚动变形机制激活的。 在没有软基质的情况下，建立了一个线性梁格模型来描述周期单元的自由动态响应。 在对被动自由度进行静态凝聚后，应用了一个通用程序，在主动自由度的低维空间中施加自由波传播的准周期条件。 通过将精确的色散曲线与从Floquet-Bloch理论产生的特征问题的渐近摄动解中得到的显式但近似的色散函数进行比较，分析了不同机械参数对带结构的影响。 概述了一个用于制定和求解摄动方程的一般方案，该方案取决于所需的近似阶数和摄动向量的维度。 在参数空间的广阔区域内，对于低阶渐近解，实现了令人满意的近似精度。 色散函数对主要参数（包括单元长宽比、连接件细长比和环密度）的显式依赖关系，使得能够深入讨论并从设计角度精细评估光谱特性，包括波速和带隙幅度等特定特征。 显示英文摘要

摘要： The engineered class of anti-tetrachiral cellular materials is phenomenologically characterized by a strong auxeticity of the elastic macroscopic response. The auxetic behavior, accompanied by a marked anisotropy, is activated by rolling-up deformation mechanisms developed by the periodic pattern of stiff rings and flexible ligaments realizing the material micro-structure. In the absence of a soft matrix, a linear beam lattice model is formulated to describe the free dynamic response of the periodic cell. After a static condensation of the passive degrees-of-freedom, a general procedure is applied to impose the quasi-periodicity conditions of free wave propagation in the low-dimension space of the active degrees-of-freedom. The effects of different mechanical parameters on the band structure are analyzed by comparing the exact dispersion curves with explicit, although approximate, dispersion functions, obtained from asymptotic perturbation solutions of the eigenproblem rising up from the Floquet-Bloch theory. A general scheme for the formulation and solution of the perturbation equations is outlined, for the desired approximation order and depending on the dimension of the perturbation vector. A satisfying approximation accuracy is achieved for low-order asymptotic solutions in wide regions of the parameter space. The explicit dependence of the dispersion functions on the main parameters, including the cell aspect ratio, the ligament slenderness and the ring density, allows the in-depth discussion and - in a design perspective - the fine assessment of the spectrum properties, including specific features like wave velocities and band gap amplitudes.