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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.

During the research of the stability of mechanical systems under loading conditions by non-conservative forces, the phenomena are encountered that are not typical for ordinary problems of mechanics (an unusual effect of friction, non-convexity, non-simply connectedness of the stability region in the space of loading parameters, etc.). The research was made of the stability of a cantilever rod under the action of compressive forces - constant potential and follower (taking into account the pulsations of the latter). A harmonic law of change in the value of the following force has been adopted. Using the methods of the Floquet theory, the parametric vibrations of the system are analyzed with the study of the position of the boundaries of the stability region on the plane of loading parameters. The nature of the system motion in the vicinity of the boundaries of the stability region is determined.

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