scholarly journals Nonlinear normal modes for damped geometrically nonlinear systems: Application to reduced-order modelling of harmonically forced structures

2006 ◽  
Vol 298 (4-5) ◽  
pp. 958-981 ◽  
Author(s):  
C. Touzé ◽  
M. Amabili
Keyword(s):  
Nonlinear Systems ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Geometrically Nonlinear ◽  
Reduced Order ◽  
Reduced Order Modelling ◽  
Nonlinear Normal

scholarly journals Evaluation of Geometrically Nonlinear Reduced-Order Models with Nonlinear Normal Modes

AIAA Journal ◽  
2015 ◽  
Vol 53 (11) ◽  
pp. 3273-3285 ◽  
Author(s):  
Robert J. Kuether ◽  
Brandon J. Deaner ◽  
Joseph J. Hollkamp ◽  
Matthew S. Allen
Keyword(s):  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Geometrically Nonlinear ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Nonlinear Normal

scholarly journals Identifying the significance of nonlinear normal modes

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160789 ◽  
Author(s):  
T. L. Hill ◽  
A. Cammarano ◽  
S. A. Neild ◽  
D. A. W. Barton
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Analytical Investigation ◽  
Nonlinear Normal ◽  
Definition Of ◽  
Forced Responses ◽  
Insight Into

Nonlinear normal modes (NNMs) are widely used as a tool for understanding the forced responses of nonlinear systems. However, the contemporary definition of an NNM also encompasses a large number of dynamic behaviours which are not observed when a system is forced and damped. As such, only a few NNMs are required to understand the forced dynamics. This paper firstly demonstrates the complexity that may arise from the NNMs of a simple nonlinear system—highlighting the need for a method for identifying the significance of NNMs. An analytical investigation is used, alongside energy arguments, to develop an understanding of the mechanisms that relate the NNMs to the forced responses. This provides insight into which NNMs are pertinent to understanding the forced dynamics, and which may be disregarded. The NNMs are compared with simulated forced responses to verify these findings.

scholarly journals Bayesian model updating of nonlinear systems using nonlinear normal modes

2018 ◽  
Vol 25 (12) ◽  
pp. e2258 ◽  
Author(s):  
Mingming Song ◽  
Ludovic Renson ◽  
Jean-Philippe Noël ◽  
Babak Moaveni ◽  
Gaetan Kerschen
Keyword(s):  
Nonlinear Systems ◽  
Bayesian Model ◽  
Model Updating ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Nonlinear Normal
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