Harmonic Balance and Averaging Techniques for Stick-Slip Limit-Cycle Determination in Mode-Coupling Friction Self-Excited Systems

Abstract

A minimal model for mode-coupling friction induced instability with Coulomb-type frictional nonlinearity is set up to investigate the applicability and quality of approximative methods to determine the limit cycles of unstable system configurations. It turns out that - due to the multi-degree-of-freedom nature of the mode-coupling instability - harmonic balance approaches yield reasonable results only if applied carefully, i.e. with respect to the special effects of the nonlinearities under consideration. The Krylov-Bogoliubov-Mitropolsky approach yields good results in a straightforward manner, the technique is however formally much more cumbersome.