论文标题
完全非线性质量质量链的通气模式
Breather modes of fully nonlinear mass-in-mass chains
论文作者
论文摘要
我们提出了一个由非线性弹簧结合的颗粒链的模型，其中每个质量都有内部质量，所有相互作用都假定为非线性。我们展示了如何使用多个时间尺度构建该系统的渐近解决方案，即通过重复应用一致性条件的耦合方程的系统解。我们的结果表明，对于非线性的某些组合，动力学由NLS控制，就像在更常见的质量链链中，内部和外部质量之间的线性相互作用。但是，当两个非线性具有二次成分时，我们表明渐近减少会导致金茨堡 - 兰道方程而不是NLS。
We propose a model for a chain of particles coupled by nonlinear springs in which each mass has an internal mass and all interactions are assumed to be nonlinear. We show how to construct an asymptotic solution of this system using multiple timescales, the systematic solution of coupled equations by repeated application of a consistency condition. Our results show that for some combinations of nonlinearity the dynamics are governed by the NLS as in the more usual mass-in-mass chains with linear interactions between inner and outer masses. However, when both nonlinearities have quadratic components, we show that the asymptotic reduction results in a Ginzburg-Landau equation instead of NLS.
