Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques

Maxime Peeters (1) , Régis Viguié (1) , Guillaume Sérandour (1) , Gaëtan Kerschen (1) , Jean-Claude Golinval (1)

1 Structural Dynamics Research Group

The concept of nonlinear normal modes (NNMs) is discussed in the present paper and its companion, Part I. One reason of the still limited use of NNMs in structural dynamics is that their computation is often regarded as impractical. However, when resorting to numerical algorithms, we show that the NNM computation is possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems. The proposed algorithm relies on two main techniques, namely a shooting procedure and a method for the continuation of NNM motions. The algorithm is demonstrated using four different mechanical systems, a weakly and a strongly nonlinear two-degree-of-freedom system, a simplified discrete model of a nonlinear bladed disk and a nonlinear cantilever beam discretized by the finite element method.

Mots clés: Nonlinear dynamics; Nonlinear normal modes; Modal analysis; Shooting method; Continuation methods of periodic motions

Domaines: Vibrations [physics.class-ph]

Maxime Peeters, Régis Viguié, Guillaume Sérandour, Gaëtan Kerschen, Jean-Claude Golinval. Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques. Mechanical Systems and Signal Processing, 2009, 23 (1), pp.195-216. ⟨10.1016/j.ymssp.2008.04.003⟩. ⟨hal-01581480⟩