scholarly journals Parametric Vibration Analysis of Pipes Conveying Fluid by Nonlinear Normal Modes and a Numerical Iterative Approach

2019 ◽  
Vol 11 (1) ◽  
pp. 38-52
Author(s):  
Feng Liang
Keyword(s):  
Vibration Analysis ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Parametric Vibration ◽  
Iterative Approach ◽  
Pipes Conveying Fluid ◽  
Nonlinear Normal ◽  
Conveying Fluid

Forced Response Analysis of Pipes Conveying Fluid by Nonlinear Normal Modes Method and Iterative Approach

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
Feng Liang ◽  
Xiao-Dong Yang ◽  
Ying-Jing Qian ◽  
Wei Zhang
Keyword(s):  
Normal Modes ◽  
Harmonic Balance Method ◽  
Nonlinear Normal Modes ◽  
Forced Response ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Iterative Approach ◽  
Pipes Conveying Fluid ◽  
Nonlinear Normal ◽  
Conveying Fluid

The forced vibration of gyroscopic continua is investigated by taking the pipes conveying fluid as an example. The nonlinear normal modes and a numerical iterative approach are used to perform numerical response analysis. The nonlinear nonautonomous governing equations are transformed into a set of pseudo-autonomous ones by using the harmonic balance method. Based on the pseudo-autonomous system, the nonlinear normal modes are constructed by the invariant manifold method on the state space and substituted back into the original discrete equations. By repeating the above mentioned steps, the dynamic responses can be numerically obtained asymptotically using such iterative approach. Quadrature phase difference between the general coordinates is verified for the gyroscopic system and traveling waves instead of standing waves are found in the time-domain complex modal analysis.

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.

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

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.

Nonlinear normal modes for the Toda Chain

1982 ◽  
Vol 45 (2) ◽  
pp. 157-209 ◽  
Author(s):  
W.E. Ferguson ◽  
H. Flaschka ◽  
D.W. McLaughlin
Keyword(s):  
Normal Modes ◽  
Toda Chain ◽  
Nonlinear Normal Modes ◽  
Nonlinear Normal
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