Linear and Nonlinear Elastic Waves in Magnetogranular Chains

We study a magnetogranular chain composed of stainless-steel beads which are placed inside an appropriately 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-rotational 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 beating in the 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 for second-harmonic generation with longitudinal waves. This magnetosensitive 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.