Resonantly Excited Normal Modes and Shear Melting of a Nonequilibrium Pattern

We find that the square patterns formed in a vertically oscillating granular layer exhibit dynamics like those of a two-dimensional (2D) square lattice coupled by Hookian springs. Different transverse normal modes of the granular lattice are resonantly excited for different container frequencies ($f_d$) and accelerations. The amplitude of a mode can be further excited by either frequency modulation of $f_d$ or reduction of friction between the grains and the plate. When the mode amplitude becomes large, the lattice melts (disorders), in accord with the Lindemann criterion for melting in 2D.