About the stability of nonconservative undamped elastic systems:some new elements

Jean Lerbet (1) , Elie Absi , Alain Rigolot (2)

1 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
2 LMM - Laboratoire de modélisation en mécanique

It is well-known that the domains of static stability and dynamic stability (even for a linear approach) do not match each other when the system is no more conservative and the dynamic approach is usually privileged, meaning that the dynamic stability domain is included in the static one. Following previous works proposing a new criterion of static stability of nonconservative systems and prolonging a paper of Gallina devoted to linear dynamic instability (flutter), we show in this paper some remarkable relations between the two approaches: contrary to the common thought, the new static stability criterion implies partially the dynamic one.

Mots clés: stiffness matrix; mixed perturbation; dynamic stability; static stability; Nonconservative systems

Domaines: Robotique [cs.RO]; Système multi-agents [cs.MA]; Automatique; Mécanique [physics.med-ph]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]; Automatique / Robotique

Jean Lerbet, Elie Absi, Alain Rigolot. About the stability of nonconservative undamped elastic systems:some new elements. International Journal of Structural Stability and Dynamics, 2009, 9 (2), pp.357--367. ⟨10.1142/S0219455409003065⟩. ⟨hal-00342816⟩