边界载荷对层级椭圆穿孔板超材料带隙的影响

摘要/Abstract

摘要： 为探索边界载荷对超材料带隙特性的影响,本文构建了一种层级椭圆穿孔板超材料,将载荷直接作用于结构的边界,采用有限元法研究了边界载荷导致结构变形所引起的带隙变化。建立了3个层级椭圆穿孔板有限元模型,将三维椭圆穿孔板简化为二维平面结构,以便于研究结构的面内带隙特性。分析了有无边界载荷作用时层级椭圆穿孔板的带隙特性、传输损耗和带隙边界对应的振型。结果表明,引入层级设计可降低带隙频率,施加边界载荷可打开更多完全带隙和方向带隙,从而更好地抑制弹性波传播,为穿孔板类超材料设计提供了一种新思路。

关键词: 边界载荷, 层级, 椭圆穿孔板, 超材料, 有限元法, 带隙

Abstract: A hierarchical elliptical perforated-panel metamaterial (HEPMM) is proposed to investigate the effect of boundary load on its bandgaps (BGs). In this research, the boundary load was applied directly to the boundary of HEPMM, and the finite element method was adopted to study the effect of BGs with structural deformation which caused by the boundary load. Three-dimensional finite element models of different hierarchical elliptical perforated panels were established, and simplified into two-dimensional structure to investigate the in-plane bandgap characteristics conveniently. Then, the bandgap characteristics, transmission loss and different vibration modes of HEPMM with and without boundary load were simulated and analyzed. According to the results, the BGs frequencies are reduced by introducing hierarchy. Meanwhile, full BGs and directional BGs are additionally opened under boundary load, thus the propagation of elastic wave is suppressed effectively. The study provides a new idea to design perforated-panel metamaterial.

Key words: boundary load, hierarchy, elliptical perforated-panel, metamaterial, finite element method, bandgap

中图分类号:

O328

张祖坚, 郭辉, 王晓玮, 袁涛, 孙裴. 边界载荷对层级椭圆穿孔板超材料带隙的影响[J]. 人工晶体学报, 2023, 52(2): 261-270.

ZHANG Zujian, GUO Hui, WANG Xiaowei, YUAN Tao, SUN Pei. Effect of Boundary Load on Bandgaps of Elliptical Perforated-Hierarchical Panel Metamaterials[J]. JOURNAL OF SYNTHETIC CRYSTALS, 2023, 52(2): 261-270.

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