Backbone transitions and invariant tori in forced micromechanical oscillators with optical detection

Abstract

Micromechanical oscillators often display rich dynamics due to nonlinearities in their response, actuation, and detection. This paper investigates the complicated response of a forced micromechanical oscillator. In particular, we investigate a thermally induced transition in the resonant response of a forced micromechanical oscillator with optical detection; and the branches of invariant tori formed at subsequent bifurcations that occur with increasing laser power. We use perturbation theory and continuation algorithms to investigate and compute these branches of invariant tori. The results of both methods are compared.