Response of parametrically driven nonlinear coupled oscillators with application to micromechanical and nanomechanical resonator arrays

The response of a coupled array of nonlinear oscillators to parametric excitation is calculated in the weak nonlinear limit using secular perturbation theory. Exact results for small arrays of oscillators are used to guide the analysis of the numerical integration of the model equations of motion for large arrays. The results provide a qualitative explanation for a recent experiment [Buks and Roukes, J. Microelectromech. Syst. 11, 802 (2002)] involving a parametrically excited micromechanical resonator array. Future experiments are suggested which could provide quantitative tests of the theoretical predictions.