Chaotic and periodic motion of a non-linear oscillator in relation with flow-induced vibrations of loosely supported tubes

Rather recently it was realized that flow-induced vibration of loosely supported tubes can depict a large variety of dynamical behaviours, including periodic and chaotic motions. Furthermore, impact forces and sliding velocities can change significantly according to the vibratory regime which is selected by the non-linear system. This complex problem is investigated here from a theoretical point of view, by using a simplified model defined as a single degree of freedom system impacting on elastic supports, depending also on the case it is provided with damping or not. Both analytical and numerical approaches are used.