Vibrations of a system of two protractile elements with plays taken into consideration

Abstract

A description of the play, that may be applied to many other problems, is the basis of the model of a beam system presented in this paper. Equations describing the motion of the system of spring elements under dynamic load have been derived taking into consideration the play occurring between the elements. The equations have been derived according to the Hamilton's variational principle. The play has been treated as a force interacting between the elements whose value depends non-linearly on the mutual distance of the contact places. The function that defines the elements' interacting force may be easily enriched with elements responsible for the energy dissipation, ego friction. The value of the method presented was proved by the carried out comparative analysis. The equation obtained has been used for an exanlple which the finite elements method (modal technique) has been applied too for comparison. In order to make the comparison more complete, the calculations have been performed not only for the beam model but for a full spatial model as well (basing on the shell model).