Transversal-rotational and zero group velocity modes in tunable   magneto-granular phononic crystals
  We report on the design and operation of a 1D magneto-granular phononic crystal composed of a chain of steel spherical beads on top of permanent magnets. The magnetic field of the permanent magnets induces forces in the granular structure. By changing its strength, we can tune the dynamic response of the granular structure. We present experimental results with evidence of coupled transversal-rotational modes, and zero group velocities modes. These observations are well supported by a proposed model taking into account the mechanical coupling between the beads and the magnets by linear stiffnesses and including all degrees of freedom in translations and rotations. 
F. Allein, V. Tournat, V.E. Gusev, and G. Theocharis
cond-mat.mtrl-sci