We are studying the dynamics of large arrays of coupled nonlinear nanomechanical oscillators. Our study is motivated by a recent experiment by Eyal Buks and Michael Roukes [1] involving a parametrically-excited nanomechanical resonator array. Previous analytical calculations using secular perturbation theory [2] were limited to small arrays of a few resonators. Here we extend the analytical treatment to large discrete systems and find that the parametric instability of these systems exhibits nontrivial behavior which takes on a different form than in other well-known nonlinear systems (e.g. Rayleigh-Benard convection). In particular, we show that different modes of the system undergo different types of bifurcation, and discuss the possible experimental consequences of this behavior. 

[1] E. Buks and M.L. Roukes, J. MEMS 11, 802 (2002).
[2] R. Lifshitz and M.C. Cross, Phys. Rev. B 67, 134302 (2003).