Fitting Measured Frequency Response Using Non-Linear Modes

Gibert, Claude

doi:10.1006/mssp.2002.1562

Cited by 33 publications

(32 citation statements)

References 3 publications

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“…Another test strategy that identifies nonlinearities in modal space using the RFS method is discussed in [13]. Alternatively, a nonlinear modal identification approach based on the single nonlinear resonant mode concept [14,15] and on a first-order frequency-domain approximation is proposed and applied in [16][17][18][19]. The forced frequency responses are expressed as a combination of a resonant nonlinear mode response and of linear contributions from the remaining modes.…”

Section: Introductionmentioning

confidence: 99%

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Peeters

Kerschen

Golinval

2011

Journal of Sound and Vibration

158

167

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a b s t r a c tModal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis (EMA) methodology of nonlinear mechanical structures. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes (LNMs). A nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single NNM during the experiments. With the help of time-frequency analysis, the energy dependence of NNM modal curves and their frequencies of oscillation are then extracted from the time series. The proposed methodology is demonstrated using two numerical benchmarks, a two-degree-of-freedom system and a planar cantilever beam with a cubic spring at its free end.

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Section: Introductionmentioning

confidence: 99%

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Peeters

Kerschen

Golinval

2011

Journal of Sound and Vibration

158

167

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“…There are, however, very few attempts to develop practical modal testing of nonlinear structures. In this context, a nonlinear modal identification approach based on the single nonlinear resonant mode concept [9,10] and on a first-order frequency-domain approximation was proposed and applied in [11][12][13][14]. The forced frequency responses are expressed as a combination of a resonant nonlinear mode response and of linear contributions from the remaining modes.…”

Section: Introductionmentioning

confidence: 99%

Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration

Peeters

Kerschen

Golinval

2011

Mechanical Systems and Signal Processing

143

105

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a b s t r a c tRealizing that nonlinearity is a frequent occurrence in engineering structures and that linear experimental modal analysis (EMA) is of limited usefulness in this context, the present paper is an attempt to develop nonlinear EMA by targeting the extraction of nonlinear normal modes (NNMs) from time series of nonlinear mechanical systems. Based on a nonlinear extension of phase resonance testing, the proposed methodology excites the structure to isolate a single NNM during the experiments. Thanks to the invariance principle, the energy dependence of that nonlinear mode (i.e., the NNM modal curves and their oscillation frequencies) can be extracted from the resulting free decay response using time-frequency analysis. This paper is devoted to the experimental demonstration and robustness of this procedure. To this end, an experimental cantilever beam with a geometrical nonlinearity is considered, and the ability of the proposed methodology to extract its NNMs from the measured responses is assessed.

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“…As mentioned in the introduction, not only does the method aim at significantly reducing the number of DOFs retained in the reduced-order model, but it also allows to handle cases of neighboring resonant modes, where standard nonlinear modes superposition is known to fail [50,51]. When mode superposition is used to compute the response, the generalized coordinates corresponding to the nonlinear modes are assumed to vary independently of each other, hence the poor accuracy of the method when two close modes have a significant contributions and can interact through the nonlinearities.…”

Section: Forced Response Synthesis Of the Tuned Modelmentioning

confidence: 99%

“…(29), the modal parameters ω n , β n , and ϕ n k , are obtained by computing the nonlinear complex modes of the whole system, without substructuring. The interested reader is referred to [50,51,6,7] for further information concerning nonlinear mode synthesis.…”

Section: Forced Response Synthesis Of the Tuned Modelmentioning

confidence: 99%

A nonlinear component mode synthesis method for the computation of steady-state vibrations in non-conservative systems

Joannin

Chouvion

Thouverez

et al. 2017

Mechanical Systems and Signal Processing

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a b s t r a c tThis paper presents an extension to classic component mode synthesis methods to compute the steady-state forced response of nonlinear and dissipative structures. The procedure makes use of the nonlinear complex modes of each substructure, computed by means of a modified harmonic balance method, in order to build a reduced-order model easily solved by standard iterative solvers. The proposed method is applied to a mistuned cyclic structure subjected to dry friction forces, and proves particularly suitable for the study of such systems with high modal density and non-conservative nonlinearities.

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Fitting Measured Frequency Response Using Non-Linear Modes

Cited by 33 publications

References 3 publications

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration

A nonlinear component mode synthesis method for the computation of steady-state vibrations in non-conservative systems

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