Emerging mechanical topological insulators based on Quantum Valley Hall Effect (QVHE) offer a myriad of unconventional and robust properties in controlling wave motion. Designing mechanical topological insulators requires a careful assignment of the system’s mechanical properties in a specific manner. Consequently, modulating the topological property of a fabricated system is typically challenging. Here, we introduce an externally adding-on mechanism that enables high tunability of QVHE without the need to alter the main fabricated structure. Specifically, we exploit a periodic elastic foundation to control the topological property of a hexagonal lattice. Non-equal stiffnesses of the elastic foundation break the inversion symmetry of the hexagonal lattice, thus introducing the QVHE to the system. A mathematical framework is established to understand the fundamental mechanism and design the topologically protected waveguides by tuning the elastic foundation. The achieved topological insulators exhibit high tolerance over defects. The paradigm in this work opens promising avenues for mechanical metamaterials with tunable topological properties.

基于量子谷霍尔效应（QVHE）的新兴机械拓扑绝缘体在控制波动方面具有无与伦比的鲁棒性。设计机械拓扑绝缘体需要以特定方式仔细分配系统的机械性能。因此，调制装配式系统的拓扑特性通常具有挑战性。在这里，我们介绍了一种外部附加机制，可实现QVHE的高可调性，而无需更改主要制造的结构。具体来说，我们利用周期性弹性基础来控制六边形格子的拓扑特性。弹性基础的不相等的刚度破坏了六角形晶格的反对称性，从而将QVHE引入系统。建立数学框架以了解基本机理并通过调整弹性基础来设计受拓扑保护的波导。所获得的拓扑绝缘体显示出对缺陷的高耐受性。这项工作的范式为具有可调拓扑特性的机械超材料开辟了广阔的前景。