AN experimental and numerical analysis of chaotic motion in vibration with impact

The flow-induced vibrations of loosely supported structures occasionally show chaotic behaviour due to the impact non-linearities at the supports ([1, 2, 3]). In the work presented here, this phenomenon was studied both experimentally and numerically in order to test the ability of computer methods to predict chaos in such systems. The experimental apparatus was designed to have the motion of a simple oscillator, the displacement of which is limited by elastic stops, and which is excited by an external sinusoidal force. The level and frequency of this force, as well as the gaps between oscillator and stops are systematically varied. The range of physical parameters where chaotic motion occurs are clearly identified using spectral analysis at low frequency. A numerical time-stepping integration of the equation of motion is used and the amplitudes as well as chaotic regions of parameters are compared with the experimental results. The agreement is found to be good, both in terms of the global behaviour of the system and evolution of the response.