Rozwiązanie pewnego problemu quasi-statycznej teorii bębnów

The problem solved in the present paper is that of displacement in a viscoelastic rope drum: acted on by a moving load. The inertia forces are rejected. This model is an approximation to a real rope drum if the velocity of displacement of the load is small. This method finds wide application in computation of low-speed driving wheels (KÖPE) [5, 6 and 7]. The solution of the viscoelastic problem mentioned above and presented here is an attempt to study rheologic effects in the material of a rope drum, the occurrence of which is confirmed, among other phenomena, by the damping of drum vibration and the creep of the lining. The model under consideration is composed of a cylindrical shell and a circular ring with its inner edge clamped and its outer edge attached to the shell by means of a rigid node. The solution is obtained from that for the elastic state by means of the Lee-Alfrey elastic-visco-elastic analogy [3 and 4]. The influence of the rigidity of the disks on the rotation angle of the edges of the shell is taken into consideration.
It is assumed that the action of the plates on the drum reduces to the bending moments only, there being no radial or tangential displacement of the edge. Theoretical considerations are illustrated by an example. The Voigt-Kelvin body is considered assuming that the material of the drum is incompressible. A typical case of cooperation between the drum and the rope is considered.