Stiffness Non-Linearity Classification Through Structured Response Component Analysis Using Volterra Series

Chatterjee, Animesh; Vyas, Nalinaksh S.

doi:10.1006/mssp.2000.1331

Cited by 9 publications

(4 citation statements)

References 17 publications

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“…Answers to some of these questions may be provided by looking at the distortions in measured FRFs of nonlinear systems using Bode plots (see Fig. 14), Nyquist plots (Vakakis and Ewins, 1994 [359]), Volterra series and HOFRFs (Storer and Tomlinson, 1993 [192]; Schoukens et al, 2000 [360]; Chatterjee and Vyas, 2001 [361]), frequency-domain ARX (Auto-Regressive with eXogenous inputs) models (Adams, 2002 [362]) and modulation matrices (Adams and Allemang, 1999b [234]) [FRFs of nonlinear systems are discussed at length in (Nayfeh and Mook, 1979 [28]; Worden and Tomlinson, 2001 [67])]. Because one class of nonlinearity can behave like another in a certain input-output amplitude range, the shape of the FRF is not always conclusive evidence of a particular nonlinearity.…”

Section: The Type Of the Nonlinearitymentioning

confidence: 99%

Past, present and future of nonlinear system identification in structural dynamics

Kerschen

Worden

Vakakis

et al. 2006

Mechanical Systems and Signal Processing

983

526

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This survey paper contains a review of the past and recent developments in system identification of nonlinear dynamical structures. The objective is to present some of the popular approaches that have been proposed in the technical literature, to illustrate them using numerical and experimental applications, to highlight their assets and limitations and to identify future directions in this research area. The fundamental differences between linear and nonlinear oscillations are also detailed in a tutorial.Theory is useful for drawing general conclusions from simple models, and computers are useful for drawing specific conclusions from complicated models (Bender, 2000 [1]). In the theory of mechanical vibrations, mathematical models-termed structural models-are helpful for the analysis of the dynamic behaviour of the structure being modeled.The demand for enhanced and reliable performance of vibrating structures in terms of weight, comfort, safety, noise and durability is ever increasing while, at the same time, there is a demand for shorter design cycles, longer operating life, minimisation of inspection and repair needs, and reduced costs. With the advent of powerful computers, it has become less expensive both in terms of cost and time to perform numerical simulations, than to run a sophisticated experiment. The consequence has been a considerable shift toward computer-aided design and numerical experiments, where structural models are employed to simulate experiments, and to perform accurate and reliable predictions of the structure's future behaviour.Even if we are entering the age of virtual prototyping (Van Der Auweraer, 2002 [2]), experimental testing and system identification still play a key role because they help the structural dynamicist to reconcile numerical predictions with experimental investigations. The term 'system identification' is sometimes used in a broader context in the technical literature and may also refer to the extraction of information about the structural behaviour directly from experimental data, i.e., without necessarily requesting a model (e.g., identification of the number of active modes or the presence of natural frequencies within a certain frequency range). In the present paper, system identification refers to the development (or the improvement) of structural models from input and output measurements performed on the real structure using vibration sensing devices.Linear system identification is a discipline that has evolved considerably during the last 30 years (Ljung, 1987 [3]; Soderstrom and Stoica, 1989 [4]). Modal parameter estimation-termed modal analysis-is indubitably the most popular approach to performing linear system identification in structural dynamics. The model of the system is known to be in the form of modal parameters, namely the natural frequencies, mode shapes and damping ratios. The popularity of modal analysis stems from its great generality; modal parameters can describe the behaviour of a system for any input type and any range of the input. Numerou...

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Section: The Type Of the Nonlinearitymentioning

confidence: 99%

Past, present and future of nonlinear system identification in structural dynamics

Kerschen

Worden

Vakakis

et al. 2006

Mechanical Systems and Signal Processing

983

526

View full text Add to dashboard Cite

show abstract

“…It is also emphasized that the selection of the excitation level and the excitation frequencies play an important role for accurate estimation of the parameters. The method however assumes that the cubic nonlinearity is known a-priori, which can be ascertained by a nonlinearity structure classification method [17]. …”

Section: Resultsmentioning

confidence: 99%

“…One such procedure has been detailed in an earlier research work [17], where system nonlinearity structure has been classified in to symmetric and asymmetric forms first and then for symmetric forms, a procedure based on response component separation technique, is suggested for identifying the cubic nonlinearity structure from non-polynomial structures. For Duffing oscillator, it can be shown [17] that all even order FRFs reduce to zero and only odd harmonics appear in the response spectrum. The amplitudes of the response harmonics present in up to thirdorder response component, following Eqs.…”

Section: Response Under Multi-tone Harmonic Excitationmentioning

confidence: 99%

“…These estimation procedures use the higher-order kernel transform synthesis formulations, which are valid only for polynomial type nonlinearities. For a general non-polynomial form of nonlinearity, the higher-order kernel transforms will also be dependent on excitation amplitude [17] and cannot be synthesized from Among various parameter estimation procedures investigated, method of harmonic probing [19] has been most successful mainly because the excitation can be easily generated in laboratory and the response can be analyzed without too much of signal processing, which is otherwise required for random excitation. Procedures based on harmonic probing have mainly employed single-tone excitation.…”

Section: Introductionmentioning

confidence: 99%

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Parameter estimation of Duffing oscillator using Volterra series and multi-tone excitation

Chatterjee

2010

International Journal of Mechanical Sciences

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Extraction of Opening and Closing States of Cracked Structure using Adaptive Volterra Filter Model

Prawin

Rao

2019

Procedia Structural Integrity

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Stiffness Non-Linearity Classification Through Structured Response Component Analysis Using Volterra Series

Cited by 9 publications

References 17 publications

Past, present and future of nonlinear system identification in structural dynamics

Past, present and future of nonlinear system identification in structural dynamics

Parameter estimation of Duffing oscillator using Volterra series and multi-tone excitation

Extraction of Opening and Closing States of Cracked Structure using Adaptive Volterra Filter Model

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