Nonlinear Structural Model Updating Based Upon Nonlinear Normal Modes

2018 ◽  
Author(s):  
Chris I. VanDamme ◽  
Matthew Allen ◽  
Joseph J. Hollkamp
Keyword(s):  
Structural Model ◽  
Model Updating ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Nonlinear Structural ◽  
Nonlinear Normal

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

Component Mode Synthesis Using Nonlinear Normal Modes

2003 ◽  
Author(s):  
Polarit Apiwattanalunggarn ◽  
Steven W. Shaw ◽  
Christophe Pierre
Keyword(s):  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Reduced Order Model ◽  
Component Mode Synthesis ◽  
Structural Systems ◽  
Order Model ◽  
Reduced Order ◽  
Nonlinear Structural ◽  
Fixed Interface ◽  
Nonlinear Normal

This paper describes a methodology for developing reduced-order dynamic models of nonlinear structural systems that are composed of an assembly of component structures. The approach is a nonlinear extension of the fixed-interface component mode synthesis technique developed for linear structures by Hurty and modified by Craig and Bampton. Specifically, the case of nonlinear substructures is handled by using fixed-interface nonlinear normal modes. These normal modes are constructed for the various substructures using an invariant manifold approach, and are then coupled through the traditional linear constraint modes (i.e., the static deformation shapes produced by unit interface motions). A simple system is used to demonstrate the proof of concept and show the effectiveness of the proposed procedure. Simulations are performed to show that the reduced-order model obtained from the proposed procedure outperforms the reduced-order model obtained from the classical fixed-interface linear component mode synthesis approach. Moreover, the proposed method is readily applicable to large-scale nonlinear structural systems.

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.

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