Recent advances have demonstrated that the non-Hermitian skin effect (NHSE), induced by system non-Hermiticity, can manipulate the localization of in-gap topological edge modes (TEMs) within mechanical topological insulators. This study introduces a straightforward analytical framework to elucidate the competition between NHSE and TEM localization in a classical mechanical meta-lattice, highlighting its impact on the dynamic behavior of TEMs within separate Bragg scattering band gaps (BSBGs). We propose a 1D non-Hermitian meta-lattice featuring a locally resonant system with active feedback control, characterized by a real-valued transfer function. This local resonance creates two separate BSBGs, each hosting a TEM defined by non-Hermitian bulk-edge correspondence. Our theoretical and numerical analyses reveal that the NHSE, with its asymmetric localization within the two BSBGs, can shift the localization of TEMs in distinct ways. This leads to an asymmetric phase transition, wherein one TEM can be delocalized and relocalized by tuning the transfer function, while the other maintains its initial localization. Moreover, we extend the mechanism of 1D asymmetric TEM delocalization to the non-Hermitian morphing of TEMs, showcasing notable examples such as temporal and spatial topological wave pumping with space- and time-dependent transfer functions in 1D time-varying and 2D stacked meta-lattices. This research bridges a gap between non-Hermitian mechanical constructs and their potential applications in classical mechanics, reinterpreting known topological wave control in 1D and uncovering new mechanisms in 2D.

中文翻译：

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了解基于 1D 和 2D 非埃尔米特谐振的超晶格中的拓扑模式和集肤模式变形


最近的进展表明，由系统非 Hermiticity 诱导的非 Hermitian 趋肤效应 （NHSE） 可以操纵机械拓扑绝缘体内隙内拓扑边缘模式 （TEM） 的定位。本研究引入了一个简单的分析框架来阐明经典机械超晶格中 NHSE 和 TEM 定位之间的竞争，突出了它对单独布拉格散射带隙 （BSBG） 内 TEM 动力学行为的影响。我们提出了一种一维非埃尔米特元晶格，其特点是具有主动反馈控制的局部谐振系统，其特征是实值传递函数。这种局部谐振创建了两个独立的 BSBG，每个 BSBG 都承载着一个由非厄米特体边对应定义的 TEM。我们的理论和数值分析表明，NHSE 在两个 BSBG 内的不对称定位可以以不同的方式改变 TEM 的定位。这导致了不对称相变，其中一种 TEM 可以通过调整传递函数进行离域和再定域，而另一种 TEM 保持其初始定域。此外，我们将一维不对称 TEM 离域机制扩展到 TEM 的非埃尔米特变形，展示了值得注意的例子，例如在一维时变和二维堆叠超晶格中具有空间和时间依赖性传递函数的时间和空间拓扑波泵浦。这项研究弥合了非厄米特机械结构与其在经典力学中的潜在应用之间的差距，重新解释了已知的 1D 拓扑波控制，并揭示了 2D 中的新机制。