In this paper, we report a new type of bandgap phenomenon called “amplitude-induced bandgap”, which is induced by amplitude in nonlinear metamaterials. Generally, bandgap phenomena in elastic metamaterials or phononic crystals have been achieved by the artificial unit cells which prevent wave propagation with Bragg scattering or internal resonance. However, the amplitude-induced bandgap originates from the amplitude and nonlinearity unlike previously discovered bandgap phenomena. Accordingly, the amplitude-induced bandgap is shown to exhibit various peculiar characteristics that have not been previously observed. Here, an analytic investigation about the amplitude-induced bandgap is conducted based on the perturbation approach in a nonlinear softening monoatomic chain. Also, various peculiar characteristics of the amplitude-induced bandgap are studied in detail. Numerical simulations using finite element analysis are carried out to validate the amplitude induced bandgap. In addition, the transmission characteristics of nonlinear bandgap are also analytically studied based on the recursive method and numerically verified through the simulations.

在本文中，我们报告了一种新型的带隙现象，称为“振幅引起的带隙”，它是由非线性超材料中的振幅引起的。通常，弹性超材料或声子晶体中的带隙现象已通过人造晶胞实现，该晶胞可防止由于布拉格散射或内部共振而引起的波传播。然而，与先前发现的带隙现象不同，幅度引起的带隙起源于幅度和非线性。因此，振幅引起的带隙显示出以前未曾观察到的各种特殊特性。在此，基于非线性软化单原子链中的扰动方法，对振幅引起的带隙进行了解析研究。也，详细研究了振幅引起的带隙的各种特殊特性。进行了使用有限元分析的数值模拟，以验证幅度感应带隙。此外，还基于递归方法对非线性带隙的传输特性进行了分析研究，并通过仿真进行了数值验证。