scholarly journals Reduced-order models for nonlinear vibrations of fluid-filled circular cylindrical shells: Comparison of POD and asymptotic nonlinear normal modes methods

2007 ◽  
Vol 23 (6) ◽  
pp. 885-903 ◽  
Author(s):  
M. Amabili ◽  
C. Touzé
Keyword(s):  
Nonlinear Vibrations ◽  
Cylindrical Shells ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Circular Cylindrical Shells ◽  
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 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.

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