亏损周期结构的完全离域性
Complete Delocalization in a Defective Periodic Structure
摘要：
我们报告存在稳定的，完全离域的响应制度在非线性缺陷周期性结构。在这种完全离域的状态下，尽管存在缺陷，系统表现出具有相同振幅的所有单元的同相振荡。这种消除缺陷产生的局部化可能发生在系统的自由和受迫响应中。在没有外部驱动的情况下，局域缺陷模式在某个能级处变得完全离域。在阻尼驱动系统的情况下，如果驱动幅度超过某个阈值，则可以实现完全离域。我们证明了这一现象的数值线性周期性结构中的一个和两个具有非线性回复力的缺陷单元。我们推导出封闭形式的解析表达式的发病完全离域，并讨论其发生的必要条件。
英文摘要：
We report on the existence of stable, completely delocalized response regimes in a nonlinear defective periodic structure. In this state of complete delocalization, despite the presence of the defect, the system exhibits in-phase oscillation of all units with the same amplitude. This elimination of defect-borne localization may occur in both the free and forced responses of the system. In the absence of external driving, the localized defect mode becomes completely delocalized at a certain energy level. In the case of a damped-driven system, complete delocalization may be realized if the driving amplitude is beyond a certain threshold. We demonstrate this phenomenon numerically in a linear periodic structure with one and two defective units possessing a nonlinear restoring force. We derive closed-form analytical expressions for the onset of complete delocalization and discuss the necessary conditions for its occurrence.
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