Abstract
Having recalled the kinematic structural stability (ki.s.s) issue and its solution for divergence-type instability, we address the same problem for flutter-type instability for the minimal required configuration of dimensions—meaning 3 degree of freedom systems. We first get a sufficient non optimal condition. In a second time, the complete issue is tackled by two different ways leading to same results. A first way using calculations on Grassmann and Stiefel manifolds that may be generalized for any dimensional configuration. A second way using the specific dimensional configuration is brought back to calculations on the sphere. Differences with divergence ki.s.s are highlighted and examples illustrate the results.
Highlights
Having recalled the kinematic structural stability issue and its solution for divergence-type instability, we address the same problem for flutter-type instability for the minimal required configuration of dimensions—meaning 3 degree of freedom systems
This paper deals with the so-called kinematic structural stability for the flutter of non conservative elastic discrete systems
In a previous recent paper, the ki.s.s. problematic was formulated in its generality and the solution for the divergence criterion for conservative as well as for non conservative elastic discrete systems has been given by use of two independent ways
Summary
This paper deals with the so-called kinematic structural stability (ki.s.s.) for the flutter of non conservative elastic discrete systems. (or more concisely the divergence ki.s.s.) is only conditional according to the second order work criterion: as long as the symmetric part of the stiffness matrix remains definite positive, the ki.s.s. holds and no additional kinematic constraint may destabilize the system by divergence. That means that the well adapted structure to investigate the general issue is, as already mentioned in [1] and in the introduction, the one of Grassmann manifold Grm,n(R) = Grm(Rn) = Grm(E) of all m-dimensional subspaces of E which is a m(n − m) dimensional compact manifold To conclude this paragraph, let us remind that the R-diagonalizability used criterion for uF when dim(F ) = m = 2 is. The corresponding constraint is given by any vector e3 ∈ Fk⊥,fl ∩ S(E)
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