scholarly journals Computation of damped nonlinear normal modes for large scale nonlinear systems in a self-adaptive modal subspace

2022 ◽  
Vol 162 ◽  
pp. 108082
Author(s):  
Jie Yuan ◽  
Yekai Sun ◽  
Christoph Schwingshackl ◽  
Loic Salles
Keyword(s):  
Nonlinear Systems ◽  
Large Scale ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Nonlinear Normal ◽  
Self Adaptive

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

scholarly journals Nonlinear normal modes and their application in structural dynamics

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Christophe Pierre ◽  
Dongying Jiang ◽  
Steven Shaw
Keyword(s):  
Large Scale ◽  
Invariant Manifolds ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Realistic Model ◽  
Galerkin Projection ◽  
Engineering Structures ◽  
Nonlinear Modes ◽  
Nonlinear Modal Analysis ◽  
Nonlinear Normal

Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced-order models that accurately describe the vibrations of large-scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin-based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam.

An Application of the Poincare´ Map to the Stability of Nonlinear Normal Modes

1980 ◽  
Vol 47 (3) ◽  
pp. 645-651 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Floquet Theory ◽  
Poincaré Map ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Theory Approach ◽  
Poincare Map ◽  
Linearized Stability ◽  
Nonlinear Normal ◽  
The Stability ◽  
Two Degree Of Freedom

The stability of periodic motions (nonlinear normal modes) in a nonlinear two-degree-of-freedom Hamiltonian system is studied by deriving an approximation for the Poincare´ map via the Birkhoff-Gustavson canonical transofrmation. This method is presented as an alternative to the usual linearized stability analysis based on Floquet theory. An example is given for which the Floquet theory approach fails to predict stability but for which the Poincare´ map approach succeeds.

Localized and Non-Localized Normal Modes in a Strongly Nonlinear Discrete System

1991 ◽  
Author(s):  
Alexander F. Vakakis
Keyword(s):  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Linear Vibration ◽  
Mode Localization ◽  
Linear Mode ◽  
Strongly Nonlinear ◽  
System A ◽  
Coupling Stiffness ◽  
Nonlinear Normal ◽  
Nonlinear Discrete System

Abstract The free oscillations of a strongly nonlinear, discrete oscillator are examined by computing its “nonsimilar nonlinear normal modes.” These are motions represented by curves in the configuration space of the system, and they are not encountered in classical, linear vibration theory or in existing nonlinear perturbation techniques. For an oscillator with weak coupling stiffness and “mistiming,” both localized and nonlocalized modes are detected, occurring in small neighborhoods of “degenerate” and “global” similar modes of the “tuned” system. When strong coupling is considered, only nonlocalized modes are found to exist. An interesting result of this work is the detection of mode localization in the “tuned” periodic system, a result with no counterpart in existing theories on linear mode localization.

Nonlinear Modal Analysis and Energy Localization in a Bladed Disk Assembly

2008 ◽  
Author(s):  
F. Georgiades ◽  
M. Peeters ◽  
G. Kerschen ◽  
J. C. Golinval ◽  
M. Ruzzene
Keyword(s):  
Modal Analysis ◽  
Nonlinear Oscillations ◽  
Periodic Structures ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Energy Localization ◽  
Bladed Disk ◽  
Bladed Disk Assembly ◽  
Nonlinear Modal Analysis ◽  
Nonlinear Normal

The objective of this study is to carry out modal analysis of nonlinear periodic structures using nonlinear normal modes (NNMs). The NNMs are computed numerically with a method developed in [18] that is using a combination of two techniques: a shooting procedure and a method for the continuation of periodic motion. The proposed methodology is applied to a simplified model of a perfectly cyclic bladed disk assembly with 30 sectors. The analysis shows that the considered model structure features NNMs characterized by strong energy localization in a few sectors. This feature has no linear counterpart, and its occurrence is associated with the frequency-energy dependence of nonlinear oscillations.

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