Identification of Sub- and Higher Harmonic Vibrations in Vibro-Impact Systems

Abstract

In many engineering applications vibro-impact systems play an important role for functionality like for example in percussion machines or cause undesirable effects like noise or fatigue. Also in assembled structures clearance in joints can lead to vibro-impact problems that affect the overall dynamics of the systems. Either way, the understanding and simulation of such systems is essential. Furthermore, combinations of impacts with other nonlinearities like friction or nonlinear springs are relevant in practice. This contribution examines similar methods for the investigation of springs with cubic stiffness and vibro-impact nonlinearities as well as their combination. The Harmonic Balance Method is used along with a continuation method to simulate Frequency Response Functions of the nonlinear systems. Additionally, the influence of higher harmonics and subharmonics is considered. In systems with impact or cubic spring also chaotic motions can occur depending on the parameters. The occurrence of these motions is estimated by the calculation of Lyapunov-Exponents. Their appearance is visualized in Poincaré-Maps and phase portraits. Further investigations will be carried out on the calculation of backbone curves for vibro-impact systems and systems with combined nonlinearities to capture the frequency-energy dependency of these systems.