AVERAGING METHOD FOR STRONGLY NONLINEAR OSCILLATORS WITH PERIODIC EXCITATIONS

An averaging method is developed to predict periodic solutions of strongly non-linear and harmonically forced oscillators. The analysis is restricted to the case of period-1 orbits. The original governing equation is transformed into an autonomous set of differential equations governing the energy and resonant phase variables. The form of the transformation is given by the unperturbed conservative orbits of the system. The scheme is applied to three examples, the non-linear pendulum, the single-well Duffing oscillator, and the canonical escape oscillator. For these examples, the analysis is performed by using Jacobian elliptic functions. These examples demonstrate the ability of the averaging method to predict both transient and steady-state behavior of the system. The method has been developed in view of studying the large excursions of the response of non-linear systems induced by random perturbations.