Abstract
A generalized Krylov-Bogoliubov-Mitropolsky (KBM) method is extended for the study of strongly nonlinear oscillators with slowly varying parameters. The asymptotic amplitude and phase are derived and then the asymptotic solutions of arbitrary order are obtained theoretically. Cubic nonlinear oscillators with polynomial damping are studied in detail. Three examples are considered: a generalized Van der Pol oscillator, a Rayleigh equation and a pendulum with variable length. Comparisons are also made with numerical solutions to show the efficiency and accuracy of the present method.