This work reports the amplitude-induced topological phase transition and Hall effect in nonlinear elastic waves metamaterials with local resonators. The multi scale method is employed to analyze nonlinear effects on the Bragg scattering and locally resonant band gaps. The amplitude-induced band inversion and topological edge states are numerically investigated. A spin Hall insulator is generated by a honeycomb lattice to show how the nonlinearity affects the frequencies of doubly degenerate states. By adjusting the nonlinear elastic wave amplitude, topological phase transition is achieved due to the intercellular and intracellular coupling. The transition from topological boundary states to bulk states is observed by increasing nonlinear elastic wave amplitude. Bidirectional and unidirectional transmissions of topological interface states with amplitude-induced properties can also be realized, which demonstrates robustness against both corners and defects. Furthermore, experiment is performed to support theoretical predictions of topological phase transition and Hall effect of nonlinear elastic wave.

中文翻译：

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具有局部谐振器的非线性弹性波超材料的霍尔效应和拓扑相变


这项工作报道了具有局部谐振器的非线性弹性波超材料中的振幅诱导拓扑相变和霍尔效应。采用多尺度方法分析对布拉格散射和局部谐振带隙的非线性影响。对振幅诱导的能带反转和拓扑边缘状态进行了数值研究。自旋霍尔绝缘体由蜂窝晶格产生，用于显示非线性如何影响双简并态的频率。通过调整非线性弹性波振幅，由于细胞间和细胞内耦合，实现了拓扑相变。通过增加非线性弹性波振幅来观察从拓扑边界态到体态的转变。还可以实现具有振幅诱导特性的拓扑界面状态的双向和单向传输，这证明了对拐角和缺陷的鲁棒性。此外，通过实验支持非线性弹性波的拓扑相变和霍尔效应的理论预测。