Averaging method for strongly nonlinear oscillators with periodic excitations
An averaging method is developed to predict periodic solutions of strongly nonlinear 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 nonlinear pendulum, the single-well Duffing oscillator, and the canonical escape oscillator. For these examples, the analysis is performed by using Jacobian elliptic functions.
scientific article; zbMATH DE number 707512