Finite element modelling for a beam on the Winckler type basis with variable rigidity

We study constructing a beam on the Winckler basis that is under the influence of a cross-force. This force rotates around the axis of the beam. The rigidity of this basis depends on the time variable. A general mathematical model is deduced for this type of constructions. Variational formulations of the boundary value problems in question are obtained. The finite element method is used to determine the stresses of a beam. We discuss the corresponding eigenvalue problems in order to apply the method of normal shapes. Finally, a`numerical result with practical application is presented.