On perturbation method of an oscillator single degree of freedom with mass that changes periodically and forced vibrations

Abstract

Abstract In this paper will be studied an Oscillator with Mass that changes periodically and forced vibration of a simple degree of freedom. This system related to the dynamics of cables such as stayed bridges, electricity, telephone, and others. Under normal conditions for all type of cables one would not expect galloping type of vibrations due to wind-forces. There is an exception concerns vibrations excited by a wind-field containing raindrops. As has been observed on scale models in wind-tunnels the raindrops that hit the inclined stay cable generate one or more rivulets on the surface of the cable. It will be studied in this paper an oscillator single degree of freedom with mass that changes periodically and forced vibrations. Small masses which periodically hitting and leaving to the oscillator with different velocity give a forced to the vibration. Because the small mass stay on the oscillator surface for some time then the effective mass of the oscillator will periodically vary in time. In this paper it will be studied the possibilities of the mass and the velocity of the masses which are hitting and leaving to the oscillator by using a perturbation method.