About the links between the static and dynamic stabilities.

The paper aims to present a new approach of the static stability of a structure and to compare it with spectral analysis (dynamic stability). Its is well-known that for conservative systems divergence (classical static instability) and flutter (classical dynamic instability) give same critical values of loads. It is well known too that for non conservative systems, particulary for undamped non conservative systems, (classical example of Beck column subjected to a follower force) the static approach fails : for all values of the force, the (non-symmetric) matrix of rigidity is regular. The only spectral analysis gives a critical value of the load. Introducing the concept of mixed perturbation of a structure, we propose a new criterion of (static) stability. We apply this criterion to the classical example previously cited (Beck column) and in a third part a general result about applications to flutter is proposed.