Pattern selection on granular layers under multiple frequency forcing

Parametrically driven surface waves in granular layers are experimentally s tudied. The system is excited by a two-frequency forcing function G(t) = ar sin(nwt) + a(1 - r) sin(mwt + phi). Various patterns are formed depending on the control parameters including tile relative acceleration r, the frequ ency ratio n : m, the phase difference phi, the input frequency omega, and so forth. A super hexagonal lattice(SHL) pattern is observed at f = 3 Hz, n : m = 6 : 7, phi = 20 degrees, r = 0.6, and a(= A omega (2)) = 4.48g. This pattern has a unique structure compared to those observed in liquid system s. Using the single inelastic particle model, we propose a mechanism for pa ttern selection in a granular layer under multiple frequency forcing.