Identification of Coupled Non-Linear Modes From Free Vibration Using Time-Frequency Representations

Bellizzi, Sergio; Guillemain, Philippe; Kronland‐Martinet, Richard

doi:10.1006/jsvi.2000.3407

Cited by 29 publications

(16 citation statements)

References 19 publications

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“…By substituting this ansatz into (10), averaging separately over the two fast frequencies and expressing the complex amplitudes in polar form, the slow-flow model is derived. 2 2 2 1 1 3 3 4 2 1 3 1 2 2 2 3 1 2 2 2 2 3 2 2 4 4 2 2 4 2 2 2 2 4 2 1 Figure 2 shows the comparison between the system response predicted by the CX method…”

Section: The Complexification-averaging Methodsmentioning

confidence: 99%

“…The validation of the SFMI method has been performed using data resulting from the numerical integration of the equations of motion of system (10). Four cases are analyzed, and the identified physical parameters together with their percentage error are listed in Table 1.…”

Section: Slow-flow Model Identification Methodsmentioning

confidence: 99%

“…Alternative approaches for slow flow-based identification were developed, in particular the Wigner-Ville approach described by Feldman and Braun 6 and the wavelet transform 7,8,9 . Using the Gabor transform, Bellizzi et al 10 related the slow-flow dynamics to the concept of coupled nonlinear modes.…”

Section: Introductionmentioning

confidence: 99%

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The slow-flow method of identification in nonlinear structural dynamics

et al. 2007

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The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode decomposition. The HHT has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the analysis of strongly nonlinear systems. In this paper, we attempt to provide the missing link, showing the relationship between the EMD and the slow-flow equations of the system. The slow-flow model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique, and a dynamical system described by slowly-varying amplitudes and phases is obtained. These variables can also be extracted directly from the experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the experimental and analytical results forms the basis of a nonlinear system identification method, termed the slow-flow model identification method, which is demonstrated using numerical examples.

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Section: The Complexification-averaging Methodsmentioning

confidence: 99%

Section: Slow-flow Model Identification Methodsmentioning

confidence: 99%

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The slow-flow method of identification in nonlinear structural dynamics

et al. 2007

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“…The first step in ERA for modal parameter extraction is to formulate the Hankel matrix H from the set of discrete cross-correlation functions at kth instant of time, h(k) [11]. The cross-correlation function is given by…”

Section: Modal Parameter Identification Techniquementioning

confidence: 99%

“…In this the magnitude and the phase of a complex FRF are used to identify coupled modes even with an incomplete measurement. Bellizzi et al [11] presented a method for identifying the non-linear modal parameters of a multidegree-of-freedom mechanical system based on time-frequency representations. The free response has been expressed as a linear combination of frequency-and amplitude-modulated components.…”

Section: Introductionmentioning

confidence: 99%

Parameter identification of torsionally coupled shear buildings from earthquake response records

Hegde

Sinha

2008

Earthq Engng Struct Dyn

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SUMMARYThis paper presents an efficient procedure to determine the natural frequencies, modal damping ratios and mode shapes for torsionally coupled shear buildings using earthquake response records. It is shown that the responses recorded at the top and first floor levels are sufficient to identify the dominant modal properties of a multistoried torsionally coupled shear building with uniform mass and constant eccentricity even when the input excitation is not known. The procedure applies eigenrealization algorithm to generate the state-space model of the structure using the cross-correlations among the measured responses. The dynamic characteristics of the structure are determined from the state-space realization matrices. Since the mode shapes are obtained only at the instrumented floor (top and first floors) levels, a new mode shape interpolation technique has been proposed to estimate the mode shape coefficients at the remaining floor levels. The application of the procedure has been demonstrated through a numerical experiment on an eight-storied torsionally coupled shear building subjected to earthquake base excitation. The results show that the proposed parameter identification technique is capable of identifying dominant modal parameters and responses even with significant noise contamination of the response records.

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2011

Hilbert Transform Applications in Mechanical Vibration

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Identification of Coupled Non-Linear Modes From Free Vibration Using Time-Frequency Representations

Cited by 29 publications

References 19 publications

The slow-flow method of identification in nonlinear structural dynamics

The slow-flow method of identification in nonlinear structural dynamics

Parameter identification of torsionally coupled shear buildings from earthquake response records

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