Free vibrations and stability of a geometrically nonlinear cantilever column loaded by a follower force directed towards the positive pole supported at the loaded end by a spring

The formulation and solution to stability problem and free vibrations of the geometrically non-linear system loaded by the follower force directed towards the positive pole is presented in the paper. The system is supported at the loaded end by a spring with linear characteristics. The boundary problem was formulated on the basis of Hamilton’s principle and, owing to its non-linearity, on the use of the straightforward expansion method. Bifurcation force and characteristic curves (in the plane: load − free vibration frequency) have been determined on the basis solution of boundary value problem. Calculations have been carried out at difference physical and geometrical parameters of considered systems.