Discrete breathers in a mass-in-mass chain with Hertzian local resonators.
Discrete breathers in a mass-in-mass chain with Hertzian local resonators.
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质中质量链中的离散呼吸器与赫兹局部谐振器。
DOI：
10.1103/physreve.95.022904
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
N. Boechler
中科院分区：
文献类型：
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作者：
S. P. Wallen;J. Lee;D. Mei;Christopher Chong;Panos Kevrekidis;N. Boechler
我们报告了一维、质量中质量链中离散呼吸器的存在，具有线性位点间耦合和非线性、预压缩赫兹局部谐振器，这是由最近对粘附到弹性基底的微球动力学的研究推动的。在理论上预测了位点间耦合的连续谱和反连续谱极限中离散呼吸器的存在之后，我们使用数值延拓来计算在有限链中的两个状态之间插值的一系列呼吸器，其中呼吸器的位移分布集中在一个晶格位置周围。然后，我们通过对上带隙边缘附近系统的线性本征模（消失幅度）解进行数值延拓来分析呼吸器的频率-幅度依赖性。最后，我们使用运动方程的直接数值积分来演示在节能和耗散场景中识别的局部模式的形成和演化，包括可能与未来实验研究相关的设置。
We report on the existence of discrete breathers in a one-dimensional, mass-in-mass chain with linear intersite coupling and nonlinear, precompressed Hertzian local resonators, which is motivated by recent studies of the dynamics of microspheres adhered to elastic substrates. After predicting theoretically the existence of discrete breathers in the continuum and anticontinuum limits of intersite coupling, we use numerical continuation to compute a family of breathers interpolating between the two regimes in a finite chain, where the displacement profiles of the breathers are localized around one lattice site. We then analyze the frequency-amplitude dependence of the breathers by performing numerical continuation on a linear eigenmode (vanishing amplitude) solution of the system near the upper band gap edge. Finally, we use direct numerical integration of the equations of motion to demonstrate the formation and evolution of the identified localized modes in energy-conserving and dissipative scenarios, including within settings that may be relevant to future experimental studies.