Numerical computation of nonlinear normal modes in mechanical engineering

Ludovic Renson (1) , Gaëtan Kerschen (2) , Bruno Cochelin (3)

1 University of Bristol [Bristol]
2 Université de Liège
3 ECM - École Centrale de Marseille

This paper reviews the recent advances in computational methods for nonlinear normal modes (NNMs). Different algorithms for the computation of undamped and damped NNMs are presented, and their respective advantages and limitations are discussed. The methods are illustrated using various applications ranging from low-dimensional weakly nonlinear systems to strongly nonlinear industrial structures.

Mots clés: periodic orbits; nonlinear normal modes; numerical methods; invariant manifolds; numerical continuation

Domaines: Systèmes dynamiques [math.DS]; Ingénierie, finance et science [cs.CE]

Ludovic Renson, Gaëtan Kerschen, Bruno Cochelin. Numerical computation of nonlinear normal modes in mechanical engineering. Journal of Sound and Vibration, 2016, ⟨10.1016/j.jsv.2015.09.033⟩. ⟨hal-01380577⟩