This paper investigates the dispersion characteristics of elastic waves propagating along the thickness direction in functionally graded laminated phononic crystals (FGLPCs) containing novel auxetic metamaterials enabled by graphene origami that is created with the aid of hydrogenation. Both graphene weight fraction and hydrogen coverage which are the key parameters governing the auxetic property are nonuniformly distributed in unit cells of FGLPCs whose material properties are determined by genetic programming-assisted micromechanical models. The dispersion relations of elastic waves in the structure are obtained based on the state space approach and the method of reverberation-ray matrix. A comprehensive parametric study is conducted to discuss the effects of graphene origami weight fraction and hydrogen coverage on bulk waves in elastic solids made of the metamaterial and elastic waves in FGLPCs. It is found that introducing auxetic metamaterials into FGLPCs can effectively manipulate elastic waves. The graded distribution of weight fraction in FGLPCs can lead to bandgaps for both transverse and longitudinal waves, while a through-thickness graded pattern in hydrogen coverage can trigger broad bandgaps for longitudinal waves only with transverse waves nearly unchanged.

本文研究了功能梯度层压声子晶体 (FGLPC) 中沿厚度方向传播的弹性波的色散特性，该晶体包含借助氢化作用产生的石墨烯折纸实现的新型拉胀超材料。作为控制拉胀特性的关键参数的石墨烯重量分数和氢覆盖率均不均匀分布在 FGLPC 的晶胞中，其材料特性由遗传编程辅助微机械模型确定。基于状态空间法和混响-射线矩阵法得到了结构中弹性波的色散关系。进行了全面的参数研究，以讨论石墨烯折纸重量分数和氢覆盖率对由超材料制成的弹性固体中的体波和 FGLPC 中的弹性波的影响。发现将拉胀超材料引入 FGLPC 可以有效地操纵弹性波。FGLPC 中重量分数的梯度分布可以导致横波和纵波的带隙，而氢覆盖的全厚度梯度模式可以触发纵波的宽带隙，而横波几乎没有变化。