The regions of flutter and divergence instability of a column subjected to Beck's generalized load, taking into account the torsional flexibility of the loaded end of the column

Abstract

Investigations into a slender system subjected to Beck's generalized load taking into account two rotational springs situated at each end of the system are presented in the paper. One spring models the finite rigidity of the mounting, while the second restricts the rotation of the loaded end of the system. The regions of divergence and flutter instability of the considered system were determined using the kinetic criterion of the stability. The boundary value of the rigidity of the spring situated at the loaded end of the column was also determined. The boundary value of the rigidity separates the regions of divergence and flutter instability. In respect of the problem of vibrations, the characteristic curves in the plane: load – natural frequency were presented. All computations were carried out using the parameters of the considered system, including the rigidity of the springs and the follower coefficient of the load.