On a hybrid approximation concept for self‐excited periodic oscillations of large‐scale dynamical systems

Abstract

AbstractWhen approximating periodic solutions in the context of large‐scale dynamical systems involving strong local nonlinearities, efficiency is of special interest. Hence, the literature suggests a combination of two approximation methods for increasing the ratio of computational cost to accuracy. Within this contribution, a combination of Finite Difference and Harmonic Balance method is proposed. Due to the usage of Harmonic Balance it is shown, that the resulting equations only depend on the degrees of freedom that are affected by nonlinear forces. As an application, a self‐excited limit cycle of a chain of oscillators is approximated and results are compared against numerical time integration to highlight qualitative accuracy.