论文标题
在非线性周期性结构中的波数空间剪辑
Wavenumber-space band clipping in nonlinear periodic structures
论文作者
论文摘要
在弱非线性系统中，立方非线性对波传播的主要影响是对分散关系的振幅依赖性校正。这种现象可以表现为频移，也可以作为波数转移，具体取决于兴奋是分别作为初始条件还是边界条件。已经提出了几种模型来捕获系统受到谐波初始激发时观察到的频移。但是，这些模型与谐波边界激发不兼容，这代表了大多数实际应用中遇到的条件。为了克服这一局限性，我们提出了一个多个量表框架，以分析捕获谐波边界激发下非线性单变性链的分散关系所经历的波数转移。我们证明了波数转移会导致异常的色散校正效果，我们将其称为波数空间束带。然后，我们将框架扩展到局部振奋的周期性结构，以探讨这种现象对带隙可调性的含义。我们表明，如果在支持谐振器的内部弹簧中部署了立方非线性，则可以使用调整功能。
In weakly nonlinear systems, the main effect of cubic nonlinearity on wave propagation is an amplitude-dependent correction of the dispersion relation. This phenomenon can manifest either as a frequency shift or as a wavenumber shift depending on whether the excitation is prescribed as a initial condition or as a boundary condition, respectively. Several models have been proposed to capture the frequency shifts observed when the system is subjected to harmonic initial excitations. However, these models are not compatible with harmonic boundary excitations, which represent the conditions encountered in most practical applications. To overcome this limitation, we present a multiple scales framework to analytically capture the wavenumber shift experienced by dispersion relation of nonlinear monatomic chains under harmonic boundary excitations. We demonstrate that the wavenumber shifts result in an unusual dispersion correction effect, which we term wavenumber-space band clipping. We then extend the framework to locally-resonant periodic structures to explore the implications of this phenomenon on bandgap tunability. We show that the tuning capability is available if the cubic nonlinearity is deployed in the internal springs supporting the resonators.
