Transitions from localization to nonlocalization in strongly nonlinear damped oscillators

We present an analysis to study transition from localization to nonlocaliza tion due to damping in a strongly nonlinear oscillator. This is performed b y computing separate analytical approximations for the early (localized) an d late (nonlocalized) response of the system, and then matching these appro ximations at a transition point. Satisfactory agreement between the theoret ical results and those derived by direct numerical integrations of the equa tions of motion is noted. Due to the structure of the localized modes of th e system under consideration, this analysis can be viewed as a passage thro ugh bifurcation study. (C) 2000 Elsevier Science Ltd. All rights reserved.