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Shear to longitudinal mode conversion via second harmonic generation isstudied theoretically and computationally for plane waves in a two-dimensional,adhesive, hexagonally close-packed microscale granular medium. The modelincludes translational and rotational degrees of freedom, as well as normal andshear contact interactions. We consider fundamental frequency plane waves inall three linear modes, which have infinite spatial extent and travel in one ofthe high-symmetry crystal directions. The generated second harmonic waves arelongitudinal for all cases. For the lower transverse-rotational mode, ananalytical expression for the second harmonic amplitude, which is derived usinga successive approximations approach, reveals the presence of particularresonant and antiresonant wave numbers, the latter of which is prohibited ifrotations are not included in the model. By simulating a lattice with adhesivecontact force laws, we study the effectiveness of the theoretical analysis fornon-resonant, resonant, and antiresonant cases. This work is suitable for theanalysis of microscale and statically compressed macroscale granular media, andshould inspire future studies on nonlinear two- and three-dimensional granularsystems in which interparticle shear coupling and particle rotations play asignificant role.

Shear to longitudinal mode conversion via second harmonic generation in a two-dimensional microscale granular crystal