The Simplest Transformation Model of Deformation of a Strip Fixed on a Double-Sided Support Element via Elastic Interlayers

An extremely simplified transformation model of dynamic deformatio of a strip consisting of two sections along its length is constructed. It is based on the classical geometrically nonlinear Kirchhoff–Love rod model on the loose section, and the fixed section of finite length is considered to be attached to the rigid and fixed support element via elastic layers. On the fixed section, the deflections of the rod and interlayers are considered zero, and for displacements in the axial direction over the thicknesses of the rod and interlayers, approximations are adopted according to the Timoshenko shear model subject to the continuity conditions at the points of their junction with each other and immobility at the points of attachment of the interlayers to the support element. The conditions for the kinematic coupling of the unfixed and fixed sections of the rod are formulated, and, based on them, using the d’Alembert–Lagrange variational princinple, the corresponding equations of motion and boundary conditions, as well as the static conditions for coupling the sections, are derived for the sections under consideration.