V.I. Feodosiev’s problem on the stability of a slotted strip under potential and non-conservative loads

We consider the problem of stability analysis for a tworod system under the action of both potential and nonconservative forces. The computational model is presented in V.I. Feodosiev’s book “Selected Problems and Questions in Strength of Materials” and consists of a vertical strip with two longitudinal cuts. The lateral parts of the strip are rigidly clamped at the top, while a compressive potential force is applied to the upper movable central part. The lower part of the strip remains uncut and unconstrained. The problem reduces to a tworod system in which the two rods are not fixed at one end but are rigidly connected to each other, while at the other end one rod is clamped and the other is free and loaded by a compressive force. In the original source, the system is loaded only by a potential force, and its stability is investigated using the static method. In this work, a similar system is subjected to an additional nonconservative follower force. Various approaches are applied to determine the critical load values and the boundaries of the stability region. The divergence boundary is constructed using the static method. The flutter boundary is obtained by the dynamic method employing minimization of a function of several variables. The behavior of the characteristic exponents responsible for the loss of stability of the system is studied under different loading regimes.
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