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Combinig the harmonic balance method (HBM) and a continuation method is awell-known technique to follow the periodic solutions of dynamical systems whena control parameter is varied. However, since deriving the algebraic systemcontaining the Fourier coefficients can be a highly cumbersome procedure, theclassical HBM is often limited to polynomial (quadratic and cubic)nonlinearities and/or a few harmonics. Several variations on the classical HBM,such as the incremental HBM or the alternating frequency/time domain HBM, havebeen presented in the literature to overcome this shortcoming. Here, we presentan alternative approach that can be applied to a very large class of dynamicalsystems (autonomous or forced) with smooth equations. The main idea is tosystematically recast the dynamical system in quadratic polynomial form beforeapplying the HBM. Once the equations have been rendered quadratic, it becomesobvious to derive the algebraic system and solve it by the so-called ANMcontinuation technique. Several classical examples are presented to illustratethe use of this numerical approach.

A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions