AVERAGING METHOD FOR STRONGLY NONLINEAR OSCILLATORS WITH PERIODIC EXCITATIONS

An averaging method is developed to predict periodic solutions of stro ngly non-linear and harmonically forced oscillators. The analysis is r estricted to the case of period-1 orbits. The original governing equat ion is transformed into an autonomous set of differential equations go verning the energy and resonant phase variables. The form of the trans formation is given by the unperturbed conservative orbits of the syste m. The scheme is applied to three examples, the non-linear pendulum, t he single-well Duffing oscillator, and the canonical escape oscillator . For these examples, the analysis is performed by using Jacobian elli ptic functions. These examples demonstrate the ability of the averagin g method to predict both transient and steady-state behavior of the sy stem. The method has been developed in view of studying the large excu rsions of the response of non-linear systems induced by random perturb ations.