ABSTRACT

In the current work, we study the role of chirality and non-centrosymmetry on the nonlinear wave propagation characteristics of periodic architectured media. The considered nonlinearities arise from the higher-order inner element kinematics of the periodic media and are therefore directly related to its structural pattern. Regarding centrosymmetric designs, the frequency corrections obtained -in the context of the Lindstedt-Poincare method- suggest that chiral architectures are more sensitive to inner kinematic nonlinearities than well-known, achiral lattice designs. In particular, for hexachiral lattice designs, non-negligible frequency corrections are obtained, not only for the primal eigenmode, but also for higher-order modes, extensively modifying the linear band diagram structure. To the contrary, for achiral, triangular and square lattice designs, inner kinematic nonlinearities mainly influence the primal, lowest eigenmode, with the higher-order modes to remain practically unaffected. Non-centrosymmetric inner designs modify the linear and nonlinear wave propagation material attributes both for chiral and achiral lattice patterns. However, the frequency ranges affected are strongly lattice dependent, with hexachiral and triangular lattices to be primarily influenced in their high frequency range, contrary to square lattices, which are mainly affected in their low frequency region.

摘要

在目前的工作中，我们研究了手性和非中心对称性对周期性架构介质非线性波传播特性的作用。所考虑的非线性来自周期性介质的高阶内部元素运动学，因此与其结构模式直接相关。关于中心对称设计，在 Lindstedt-Poincare 方法的背景下获得的频率校正表明，手性结构比众所周知的非手性晶格设计对内部运动非线性更敏感。特别是，对于六手性晶格设计，获得了不可忽略的频率校正，不仅适用于原始本征模式，而且适用于高阶模式，从而广泛修改了线性能带图结构。相反，对于非手性，三角形和方形晶格设计，内部运动非线性主要影响原始的、最低的本征模态，而高阶模态实际上不受影响。非中心对称内部设计修改了手性和非手性晶格图案的线性和非线性波传播材料属性。然而，受影响的频率范围强烈依赖晶格，六手形和三角形晶格主要在其高频范围内受到影响，而方形晶格主要在其低频区域受到影响。非中心对称内部设计修改了手性和非手性晶格图案的线性和非线性波传播材料属性。然而，受影响的频率范围强烈依赖晶格，六手形和三角形晶格主要在其高频范围内受到影响，而方形晶格主要在其低频区域受到影响。非中心对称内部设计修改了手性和非手性晶格图案的线性和非线性波传播材料属性。然而，受影响的频率范围强烈依赖晶格，六手形和三角形晶格主要在其高频范围内受到影响，而方形晶格主要在其低频区域受到影响。