Bayesian model updating and class selection of a wing-engine structure with nonlinear connections using nonlinear normal modes

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.

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Data-driven identification of nonlinear normal modes via physics-integrated deep learning

Nonlinear Dynamics ◽

10.1007/s11071-021-06931-0 ◽

2021 ◽

Author(s):

Shanwu Li ◽

Yongchao Yang

Keyword(s):

Deep Learning ◽

Normal Modes ◽

Nonlinear Normal Modes ◽

Data Driven ◽

Nonlinear Normal

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

13th Biennial Conference on Mechanical Vibration and Noise: Vibration Analysis — Analytical and Computational ◽

10.1115/detc1991-0325 ◽

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.

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Nonlinear Modal Analysis and Energy Localization in a Bladed Disk Assembly

Volume 5: Structures and Dynamics, Parts A and B ◽

10.1115/gt2008-51388 ◽

2008 ◽

Cited By ~ 2

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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Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

Applied Mechanics ◽

10.1115/imece2006-14602 ◽

2006 ◽

Author(s):

M. Amabili ◽

C. Touze´ ◽

O. Thomas

Keyword(s):

Nonlinear Vibrations ◽

Circular Cylindrical Shell ◽

Equations Of Motion ◽

Normal Modes ◽

Nonlinear Normal Modes ◽

Harmonic Excitation ◽

Nonlinear Responses ◽

Nonlinear Normal ◽

The Galerkin Method ◽

Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

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