Eigenvalue method with symmetry and vibration analysis of cyclic structures

Aurélien Grolet (1) , Philippe Malbos (2) , Fabrice Thouverez (1)

1 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes
2 AGL - Algèbre, géométrie, logique

We present an application of the eigenvalue method with symmetry for solving polynomial systems arising in the vibration analysis of mechanical structures with symmetry properties. The search for solutions is conducted by the so called multiplication matrix method in which the symmetry of the system is taken into account by introducing a symmetry group and by working with the set of invariant polynomials under the action of this group. Using this method, we compute the periodic solutions of a simple dynamic system modeling a cyclic mechanical structure subjected to nonlinearities.

Mots clés: Polynomial System; Excitation Force; Vibration Analysis; Multiplication Matrix; Periodic Solution

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

Aurélien Grolet, Philippe Malbos, Fabrice Thouverez. Eigenvalue method with symmetry and vibration analysis of cyclic structures. Computer Algebra in Scientific Computing. CASC 2014., Sep 2014, Warsaw, Poland. pp.121-137, ⟨10.1007/978-3-319-10515-4_10⟩. ⟨hal-02084948⟩