On the stability of elastic systems under nonconservative follower forces

Summary We consider here the problem of the transition between stability and instability of the equilibrium configuration of a linear elastic system subjected to nonconservative follower(1) forces, when their magnitudes are affected by a common factor which is gradually increased.It is known that critical conditions for the stability of equilibrium may occur either by two natural frequencies of the system coinciding or by one natural frequency becoming zero, and that in the second eventuality they can also be recognised by the ordinary static criteria.We give evidence how, as distinct from the case of the conservative forces, the configuration considered can present itself again as stable for values of the load superior to an eventual critical load after the passing of a subsequent characteristic condition of one of the above-mentioned types and in particular of the second type.We indicate the necessity of the completion from this point of view of the treatment of a classic group of problems set by L. Collatz and A. Pflüger.Finally, we give sufficient conditions for the non-occurrence in problems of this kind of characteristic conditions of the second type.This study was presented at the meeting 19th January, 1964 of the Istituto Veneto di Scienze Lettere ed Arti and included in Vol. CXXII pp. 107–119 of the Acts of the same Institute.