We study a magneto-granular chain composed of stainless steel beads which are placed inside a properly designed periodic magnetic field. The latter provides attractive forces between the particles, leading to a stable structure, free of mechanical boundaries. Using a scanning laser-based probe at the individual-particle level, we observe experimentally, the propagation of longitudinal as well as transverse/rotation waves. In addition, we obtain the dispersion band diagram. In the linear regime, these observations are well supported by a mass-spring model that takes into account both a normal and a shear mechanical coupling between the beads considering translational and rotational degrees of freedom. In the weakly nonlinear regime, we present experimental results including the beating in amplitude of the second harmonic for the longitudinal waves and propagation under oblique driving excitation. A theoretical model that takes into account the Hertzian contact mechanics, dissipation and the finite size of the system, captures well the results of the second harmonic generation for the longitudinal waves. This magneto-sensitive system offers great freedom to design complex waveguide geometries where the interplay between geometry, wave polarization and nonlinearity may pave the way toward the development of advanced signal processing elastic devices.

中文翻译：

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磁珠链中的线性和非线性弹性波

我们研究了由不锈钢珠组成的磁粒链，这些磁珠被放置在适当设计的周期性磁场内。后者在颗粒之间提供吸引力，从而导致结构稳定，没有机械边界。在单个粒子水平上使用基于扫描激光的探针，我们通过实验观察了纵向波和横向波/旋转波的传播。另外，我们获得了色散能带图。在线性状态下，质量-弹簧模型很好地支持了这些观察，该模型考虑了平移和旋转自由度时，珠子之间的法向和剪切机械耦合。在弱非线性状态下 我们提供的实验结果包括纵波二次谐波振幅的跳动以及倾斜驱动激励下的传播。一个考虑了赫兹接触力学，耗散和系统有限尺寸的理论模型，可以很好地捕获纵波二次谐波的产生结果。该磁敏系统为设计复杂的波导几何形状提供了极大的自由度，其中几何形状，波极化和非线​​性之间的相互作用可能为高级信号处理弹性器件的开发铺平道路。很好地捕获了纵波二次谐波的生成结果。该磁敏系统为设计复杂的波导几何形状提供了极大的自由度，其中几何形状，波极化和非线​​性之间的相互作用可能为高级信号处理弹性器件的开发铺平道路。很好地捕获了纵波二次谐波的生成结果。该磁敏系统为设计复杂的波导几何形状提供了极大的自由度，其中几何形状，波极化和非线​​性之间的相互作用可能为高级信号处理弹性器件的开发铺平道路。