Influence of the supporting spring stiffness on the vibrations and atability of a geometrically non-linear column

In the paper, the non-linear vibrations and stability of a compound two-rod column with different bending rigidities of its members are investigated. The support of the column is pinned and has a rotational spring the stiffness of which can be either constant or dependent on the applied load. A perturbation technique is chosen to solve the problem. As the column is loaded by a partially follower load it loses its stability via divergence or flutter. For the case of the nonconservative load an adjoint system is formulated for finding the amplitude-frequency relation. The linear part of the natural frequency for adjoint systems is the same, but the non-linear terms differ for each system because they depend on the vibration modes. The support stiffening may lower the critical load of the column.