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

By M. Peeters, Regis Vigui'e, Guillaume Serandour, Gaetan Kerschen, Jean-Claude Golinval. 2009

541 citations recorded by the source corpus.

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.

Subfields: Civil and Structural Engineering, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/393951af3f4107acc9929156fd2b7b5a8e8a24dc

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In Civil and Structural Engineering

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Citations in the corpus

Nonlinear normal modes and spectral submanifolds: existence, uniqueness and use in model reduction (2016, background): “[36], and Avramov and Mikhlin [3, 4] for reviews).”
The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems (2014, unknown): “The shooting technique[2] consists in optimizing the initial state of the system, which is the unknown of the shooting problem, so that the signal obtained from a time integration of the equations of motion with this initial state is periodic.”
The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems (2015, methodology): “with a Newmark time integration scheme as in [3]; they serve as a reference solution.”
Evaluation of Geometrically Nonlinear Reduced-Order Models with Nonlinear Normal Modes (2015, methodology): “A recently developed numerical algorithm repeatedly integrates the equations of motion (EOMs) over one period of each mode and use shooting and pseudoarc-length continuation to very efficiently compute the NNMs of a system [3].”
Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction (2017, unknown): “(17) were used to compute the nonlinear normal modes [36] using the continuation algorithm in [41].”