Identification of nonlinear normal modes of engineering structures under broadband forcing

Noël, Jean-Philippe; Renson, Ludovic; Grappasonni, Chiara; Kerschen, Gaëtan

doi:10.1016/j.ymssp.2015.04.016

Cited by 45 publications

(26 citation statements)

References 44 publications

(68 reference statements)

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“…He also required that the definition reduced to the correct one for linear systems and provided a simple generalisation. Although the Rosenberg idea has generated a great deal of progress [9][10][11], the remainder of this paper will concentrate on the Shaw-Pierre concept.…”

Section: Rosenberg Normal Modesmentioning

confidence: 99%

A Machine Learning Approach to Nonlinear Modal Analysis

Worden

Green

2014

Dynamics of Civil Structures, Volume 4

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a b s t r a c tAlthough linear modal analysis has proved itself to be the method of choice for the analysis of linear dynamic structures, its extension to nonlinear structures has proved to be a problem. A number of competing viewpoints on nonlinear modal analysis have emerged, each of which preserves a subset of the properties of the original linear theory. From the geometrical point of view, one can argue that the invariant manifold approach of Shaw and Pierre is the most natural generalisation. However, the Shaw-Pierre approach is rather demanding technically, depending as it does on the analytical construction of a mapping between spaces, which maps physical coordinates into invariant manifolds spanned by independent subsets of variables. The objective of the current paper is to demonstrate a data-based approach motivated by Shaw-Pierre method which exploits the idea of statistical independence to optimise a parametric form of the mapping. The approach can also be regarded as a generalisation of the Principal Orthogonal Decomposition (POD). A machine learning approach to inversion of the modal transformation is presented, based on the use of Gaussian processes, and this is equivalent to a nonlinear form of modal superposition. However, it is shown that issues can arise if the forward transformation is a polynomial and can thus have a multi-valued inverse. The overall approach is demonstrated using a number of case studies based on both simulated and experimental data.

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Section: Rosenberg Normal Modesmentioning

confidence: 99%

A Machine Learning Approach to Nonlinear Modal Analysis

Worden

Green

2014

Dynamics of Civil Structures, Volume 4

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“…At present, two specific methods on experimental modal analysis are used, namely phase resonance and phase separation methods. In phase separation testing, several normal modes are excited simultaneously using either broadband or swept-sine force, and are subsequently identified using appropriate linear system identification techniques [2]. Reversely, phase resonance testing, also known as force appropriation, consists in exciting the normal modes of interest one at a time using a multi-point sine forcing at the corresponding natural frequency.…”

Section: Introductionmentioning

confidence: 99%

Vibration test method of nonlinear normal mode

Li¹,

Huang²

2018

Vib. proced.

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Experimental modal analysis is an important tool in dynamic testing. Experimental modal analysis of linear engineering structures is now mature. However, nonlinear behavior of engineering structure is a challenge. In this paper, a vibration test method of nonlinear normal mode (NNM) is studied. First, a 3-DOF test device with nonlinear stiffness is designed. Then, based on methodology of force appropriation, an approach to nonlinear modal testing is studied. Specifically, multi-harmonic sine force excitation is applied on the device and velocity response of the device is measured by laser vibrometer. According to the area in force-velocity response plot, the excitation is adjusted to stimulate nonlinearity of the device. Work of this paper explores vibration test method of NNM and can be used for identification of NNM and response prediction of the system, which lays the foundation for application in engineering structure of aero-engine.

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“…The most recent and popular contributions pursuing this goal in mechanical vibration engineering were surveyed in Ref. [Noël & Kerschen (2017)], and include, e.g., nonlinear modal analysis techniques [Chen et al (2014) ;Noël, Renson, Grappasonni, & Kerschen (2016); Peeters, Kerschen, & Golinval (2011); Renson, Gonzalez-Buelga, Barton, & Neild (2016)] and numerical model updating methods [Claeys, Sinou, Lambelin, & Alcoverro (2014); Isasa, Hot, Cogan, & Sadoulet-Reboul (2011)].…”

Section: Introductionmentioning

confidence: 99%

Grey-box state-space identification of nonlinear mechanical vibrations

Noël

Schoukens

2017

International Journal of Control

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The present paper deals with the identification of nonlinear mechanical vibrations. A grey-box, or semiphysical, nonlinear state-space representation is introduced, expressing the nonlinear basis functions using a limited number of measured output variables. This representation assumes that the observed nonlinearities are localised in physical space, which is a generic case in mechanics. A two-step identification procedure is derived for the grey-box model parameters, integrating nonlinear subspace initialisation and weighted least-squares optimisation. The complete procedure is applied to an electrical circuit mimicking the behaviour of a single-input, single-output (SISO) nonlinear mechanical system and to a single-input, multiple-output (SIMO) geometrically nonlinear beam structure.

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Identification of nonlinear normal modes of engineering structures under broadband forcing

Cited by 45 publications

References 44 publications

A Machine Learning Approach to Nonlinear Modal Analysis

A Machine Learning Approach to Nonlinear Modal Analysis

Vibration test method of nonlinear normal mode

Grey-box state-space identification of nonlinear mechanical vibrations

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