Global and bifurcation analysis of a structure with cyclic symmetry

Emmanuelle Sarrouy (1) , Aurélien Grolet (1) , Fabrice Thouverez (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

Introducing non-linearities into models contributes towards a better reality description but leads to systems having multiple solutions. It is then legitimate to look for all the solutions of such systems, that is to have a global analysis approach. However no effective method can be found in literature for systems described by more than two or three degrees of freedom. We propose in this paper a way to find all T-periodic solutions--where T is known--of a non-linear dynamical system. This method is compared to three other approaches and is shown to be the most efficient on a Duffing oscillator. As a more complex example, a rotor model including a squeeze-film damper is studied and a second branch of solutions is exhibited.

Mots clés: Global analysis; Nonlinear Normal Modes (NNM); Continuation; Bifurcation

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Emmanuelle Sarrouy, Aurélien Grolet, Fabrice Thouverez. Global and bifurcation analysis of a structure with cyclic symmetry. International Journal of Non-Linear Mechanics, 2011, 46 (5), pp.727--737. ⟨10.1016/j.ijnonlinmec.2011.02.005⟩. ⟨hal-00623630⟩