Beck’s task with a pulsating tracking force

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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