Linearized harmonic balance based derivation of slow flow for some class of autonomous single degree of freedom oscillators

In this paper we exploit the embedding of linearization in the harmonic balance method developed by Wu and its collaborators to propose an approach for deriving the slow flow for some class of damped autonomous single degree of freedom oscillators. The linearized harmonic balance method is used to compute the coefficients of the harmonics of an assumed form of the solution and to derive a system of two coupled ordinary differential equations related to the slow flow. A power series procedure is next used to decouple the coupled system and to obtain the slow flow. Two examples provided to illustrate the proposed procedure show excellent results.