Abstract: Based on the generalized harmonic balance method, the period-m responses of free and forced Duffing oscillators are constructed and compared with numerical solutions from which the effects of nonlinear term and excitation parameters can be observed. For free vibrations, the response periods are assumed to be integer times of the natural period of the corresponding linear system and the excitation period respectively. It is shown that the number of harmonic terms should be large enough for both strongly nonlinear systems and period-doubling bifurcation solutions with large period so that the approximate analytic solutions are comparative to numerical results.

Key words: generalized harmonic balance method, strong non-linearity, Duffing systems, period-m solution