Nonlinear normal modes, Part I: A useful framework for the structural dynamicist

759 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Evaluation of Geometrically Nonlinear Reduced-Order Models with Nonlinear Normal Modes (2015, background): “These types of internal resonances, between modes for which the linear frequencies are not commensurate, have received relatively little attention in the literature [7].”
Model-Based Control of Soft Robots: A Survey of the State of the Art and Open Challenges (2021, methodology): “Following a similar philosophy as the functional expansions discussed for rod models, model order reduction of FEMs can also be extended to nonlinear deformations [80], [81], [82].”
The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems (2015, methodology): “Beyond applications to classical vibration problems, HB was exploited for extending linear modal analysis to nonlinear systems [48].”
Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction (2017, positive): “(17) were used to compute the nonlinear normal modes [36] using the continuation algorithm in [41].”
The Harmonic Balance Method for Advanced Analysis and Design of Nonlinear Mechanical Systems (2014, positive): “However, it can be demonstrated that there generally exist a countable infinity of such internal resonances for nonlinear systems[28].”