Rain-Wind Induced Vibrations of a Simple Oscillator

In this paper a relatively simple mechanical oscillator is considered which may be used to study rain-wind induced vibrations of stay cables of cable-stayed bridges. In recent publications mention is made of vibrations of (inclined) stay cables which are excited by a wind-field containing rain drops. The rain drops that hit the cables generate a rivulet on the surface of the cable. The presence of flowing water on the cable changes the cross section of the cable experienced by the wind-field. A symmetric flow pattern around the cable with circular cross section may became asymmetric due to the presence of the rivulet and may consequently induce a lift-force as a mechanism for vibration. During the motion of the cable the position of rivulet (s) may vary as the motion of the cable induces an additional varying aerodynamic force perpendicular to the direction of the wind-field. It seems not to easy to model this phenomenon: several author state that there is no model available y ct. The idea to model this problem is to consider a horizontal cylinder supported by springs in such a way that only one degree of freedom i.e. vertical vibrations are possible. We consider a ridge on the surface of the cylinder parallel to the axis of the cylinder. Let additionally the cylinder with ridge be able to oscillate, with small amplitude, around the axis such that the oscillationare excited by an external force. It may be clear that the small amplitude oscillations of the cylinder and hence of the ridge induce a varying lift and drag force. In this approach it is assumed that the motion of the ridge models the dynamics of the rivulet(s) on the cable. By using a quasi-steady approach to model the aerodynamic forces one arrives at a nonlinear second order equation displaying three different kinds of excitation mechanisms: self-excitation, parametric excitation and ordinary forcing. The firstresults of the analysis of the equation of motion show that even in a linear approximation for certain values of the parameters involved stable periodic motions are possible. In the relevant cases where in linear approximation unstable periodic motions are found, results of an analysis of the nonlinear equation are presented.