Refined transformational model of deformation of a rod-strip with a fixed section on one of the front surfaces

A refined geometrically nonlinear model of static and dynamic deformation has been developed for a rod-strip which connected on one of its faces to an absolutely rigid support element of finite length. This model describes the transformation of bending forms of motion of the unfixed section into longitudinal-shear forms of motion of the fixed section. The model is based on of S.P. Timoshenko's model for the unfixed section, taking into account transverse shear and compression deformations, which is transformed into another model when transitioning from the unfixed to the fixed section. The main equations corresponding to the constructed model for the unfixed section are derived with such precision and content that, in the case of static deformation, they allow for the identification of classical buckling forms of instability (BFI) under conditions of axial compression and transverse-shear BFI under conditions of bending, while in the case of dynamic deformation, they allow for the transformation of bending forms of oscillations into forced and parametric longitudinal-transverse forms. For the formulation of linear stationary dynamic problems, the derived equations are reduced to three unconnected equations that allow for exact analytical solutions.