Job Stéphane, Santibanez Francisco, Tapia Franco, Melo Francisco
Supmeca, 3 rue Fernand Hainaut, 93407 Saint-Ouen Cedex, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):025602. doi: 10.1103/PhysRevE.80.025602. Epub 2009 Aug 24.
We report observations of mechanical energy localization in a strongly nonlinear discrete lattice. The experimental setup we consider is a one-dimensional nonloaded horizontal chain of identical spheres interacting via the nonlinear Hertz potential which contains a mass defect. Our experiments show that the interaction of a solitary wave with a light intruder excites a nonlinear localized mode. In agreement with dimensional analysis, we find that the frequency of localized oscillations exceeds the incident wave frequency spectrum and nonlinearly depends on incident wave strength and on mass and size of the intruder. The absence of tensile stress between grains allows some gaps to open, which in turn induces a significant enhancement of the amplitude of oscillations. We performed numerical simulations that precisely describe our observations without any adjusting parameters.
我们报告了在强非线性离散晶格中机械能局域化的观测结果。我们所考虑的实验装置是一维无负载的水平链条，由相同的球体通过包含质量缺陷的非线性赫兹势相互作用组成。我们的实验表明，孤立波与轻侵入体的相互作用激发了一种非线性局域模式。与量纲分析一致，我们发现局域振荡的频率超过了入射波频谱，并且非线性地依赖于入射波强度以及侵入体的质量和尺寸。颗粒间不存在拉应力使得一些间隙得以打开，这进而导致振荡幅度显著增强。我们进行了数值模拟，能精确描述我们的观测结果，且无需任何调整参数。
