The regions of divergence and flutter instability of a column subjected to beck’s generalized load taking into account an elastic support at the loaded end

The boundary value problem concerning the free vibrations of a slender system subjected to Beck’s generalized load was formulated and solved in the work. The considered column was elastically supported by a spring with linear characteristic at the loaded end. The critical load of the system, both divergence and flutter, and the regions of presence of divergence and flutter instability were determined on the basis of the boundary problem concerning the free vibrations (the kinetic criterion of stability). Numerical calculations have been assigned to different values of the parameters of the considered system for which the follower factor, the rigidity parameter of a spring supporting column, the parameter of the translational inertia of the body mounted at the loaded end of the column are ranked.