On an unduly simplified model in the non-conservative problems of elastic stability

The peculiar features of instability of Dzhanelidze's model, which is composed of a massless flexible bar and a concentrated mass at the tip and is subjected to a tangential follower force at the tip, are considered. By discussing the eigenvalue curves of Pflüger's model, which has distributed mass in addition to the case of Dzhanelidze's model, and of the corresponding discrete model, it is shown that the critical value, which one must use the dynamic method to obtain, can be identical with the classical Euler value obtainable by the static method only as a result of ignoring a crucial mass. The mathematical meaning of the infinitely large critical frequency is pertinently interpreted.