Stability of a rod with the elastic joint exposed to distributed non-conservative load

Abstract

Numerous features of non-conservative mechanical systems identified in studying their stability determine significant theoretical and practical interest to analyze various options of the calculation schemes. The paper considers stability of a rectilinear rod connected at one end to a joint and loaded with follower and potential loads uniformly distributed along the rod length. The joint was rigid with respect to rotation of the rod end. In order to apply the method of expanding solution to the perturbed motion equation into a series in terms of eigenmodes, the problem of determining the system eigenfrequencies and modes was solved. The cases of separate and combined action of the follower and potential loads were considered. A study was made on the influence of rigidity of the rod fastening and damping in the system on the loads critical values and on the position of the stability region boundaries on the loading parameters plane.