Topological insulator (TI) that possesses topologically protected characteristic of guiding the wave against disorders and structural perturbations without backscattering has attracted significant research interest in various fields including electromagnetic, acoustic and elastic system. However, for the mechanical system, realizing an elastic analogue of three-dimensional (3D) TI supporting the topologically protected wave propagation in two-dimensional (2D) plane is still a challenge due to the complicated mode polarization of elastic wave in 3D. This paper theoretically and experimentally investigates the robust and layer-selective transports of elastic wave in 3D monolayer- and bilayer-stacked plate-like metamaterial structures. Firstly, considering 3D monolayer-stacked structure, the 2D valley surface states are achieved numerically along the 2D projected plane based on the mechanism of quantum valley Hall effect. The simulation and experimental measurement are performed to confirm the robust transport of 3D elastic wave and backscattering immunity against the straight channel and sharp bends. Then, by stacking the monolayer into bilayer with a twisted angle of 60^°, non-zero interlayer coupling of elastic valley layer is introduced and the layer-related topological phase is revealed in the 3D bilayer-stacked structure, giving rise to the 2D topological layer-dependent surface states. Finally, the 3D robust layer-selective transports of elastic wave are tested by experiment. This research provides exciting application perspectives for ultrasonic devices with robustness, lower-power consumption and high-dimensional manipulation.

具有拓扑保护特性的拓扑绝缘体（TI）具有引导波免受紊乱和结构扰动而无反向散射的拓扑保护特性，在电磁，声学和弹性系统等各个领域引起了广泛的研究兴趣。然而，对于机械系统而言，由于3D弹性波的复杂模式极化，实现支持在二维（2D）平面中受拓扑保护的波传播的三维（3D）TI弹性模拟仍然是一项挑战。本文在理论和实验上研究了弹性波在3D单层和双层堆叠的板状超材料结构中的鲁棒性和层选择性传输。首先，考虑3D单层堆叠结构，基于量子谷霍尔效应的机理，沿着二维投影平面数值地获得了二维谷表面状态。进行仿真和实验测量以确认3D弹性波的稳健传输以及对直通道和锐弯的反向散射免疫力。然后，通过以60度的扭曲角度将单层堆叠为双层^°，非零夹层弹性谷层的耦合被引入并且该层有关的拓扑相显露在3D双层堆叠结构，从而产生二维拓扑层依赖性表面状态。最后，通过实验测试了弹性波的3D鲁棒层选择性传输。这项研究为具有耐用性，低功耗和高尺寸操纵的超声设备提供了令人兴奋的应用前景。