Assessment of the harmonic balance method on a self-oscillating one-degree-of-freedom system with regularized friction

Time-periodic solutions of dynamical systems can be looked for using a discretization method. This paper tests the harmonic balance method (HBM) on a one-degree-of-freedom system (mass, damper, spring, belt) with a regularized friction law. Its relative error is computed with respect to the number of discretization unknowns. Despite the widespread idea that frequency methods are hardly applicable to friction problems, the HBM compares well with a classical time-domain method for this nonlinear system. The main conclusion of this article is that the HBM, without any specific optimization, is well suited for regularized friction.