Instantaneous Indicators of Structural Behaviour Based on the Continuous Cauchy Wavelet Analysis

Argoul, Pierre; Le, Thien-Phu

doi:10.1006/mssp.2002.1557

Cited by 71 publications

(52 citation statements)

References 4 publications

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“…Also, considering the first-order approximation restricted to T 0 -scale solution (CD frequencies), the comparison with direct numerical integration solution shows that they are very different too, even in lower frequencies considering that the lower extreme values The numerical responses in fourth case, for both lateral bending motions, have been further analysed using wavelet transform (with Morlet motherwavelet) with a MATLAB tool developed in University of Liege [32,33]. In Fig.…”

Section: Comparison Of Multiple Scales Solution With Direct Numericalmentioning

confidence: 99%

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Georgiades

2017

Nonlinear Dyn

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Research on spinning shafts is mostly restricted to cases of constant rotating speed without examining the dynamics during their spin-up or spindown operation. In this article, initially the equations of motion for a spinning shaft with non-constant speed are derived, then the system is discretised, and finally a nonlinear dynamic analysis is performed using multiple scales perturbation method. The system in firstorder approximation takes the form of two coupled sets of paired equations. The first pair describes the torsional and the rigid body rotation, whilst the second consists of the equations describing the two lateral bending motions. Notably, equations of the lateral bending motions of first-order approximation coincide with the system in case of constant rotating speed, and considering the amplitude modulation equations, as it is shown, there are detuning frequencies from the Campbell diagram. The nonlinear normal modes of the system have been determined analytically up to the second-order approximation. The comparison of the analytical solutions with direct numerical simulations shows good agreement up to the validity of the performed analysis. Finally, it is shown that the Campbell diagram in the case of spin-up or spin-down operation cannot describe the critical situations of the shaft. This work paves the way, for new safe operational 'modes' of rotating structures bypassing critical situations, and F. Georgiades (B) School of Engineering, College of Science, University of Lincoln, Brayford Pool, Lincoln LN6 7TS, UK e-mail: fgeorgiadis@lincoln.ac.uk also it is essential to identify the validity of the tools for defining critical situations in rotating structures with non-constant rotating speeds, which can be applied not only in spinning shafts but in all rotating structures.

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Section: Comparison Of Multiple Scales Solution With Direct Numericalmentioning

confidence: 99%

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Georgiades

2017

Nonlinear Dyn

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“…With estimates of the transition matrix A in hand we compute its eigen values and we can identify eigen frequencies and damping factors of the vibrating system following equations (12) and (13). However, all the subspace modal identification algorithms have a serious problem of model order determination.…”

Section: H ¼ôK ð26þmentioning

confidence: 99%

“…For all functions y(t) satisfying the condition ∫ þ∞ À∞ jyðtÞj 2 dt < ∞, which implies that y(t) decays to zero at ±∞, the wavelet transform of y(t) is defined as [10][11][12][13][14][15]:…”

Section: The Continuous Wavelet Transform 41 Definition and Propertiesmentioning

confidence: 99%

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Modal parameter identification of a CMUT membrane using response data only

Lardiès

Bourbon

Moal

et al. 2017

Mechanics & Industry

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Abstract. Capacitive micromachined ultrasonic transducers (CMUTs) are microelectromechanical systems used for the generation of ultrasounds. The fundamental element of the transducer is a clamped thin metallized membrane that vibrates under voltage variations. To control such oscillations and to optimize its dynamic response it is necessary to know the modal parameters of the membrane such as resonance frequency, damping and stiffness coefficients. The purpose of this work is to identify these parameters using only the time data obtained from the membrane center displacement. Dynamic measurements are conducted in time domain and we use two methods to identify the modal parameters: a subspace method based on an innovation model of the state-space representation and the continuous wavelet transform method based on the use of the ridge of the wavelet transform of the displacement. Experimental results are presented showing the effectiveness of these two procedures in modal parameter identification.

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“…Such plots enable one to deduce the temporal evolutions of the dominant frequency components of the signals analyzed. In recent works by Argoul and co-workers [4][5][6], the Continuous Cauchy WT was applied to system identification of linear dynamical systems.…”

Section: A New Way For Multi-frequency Nonlinear Energy Transfermentioning

confidence: 99%

Multi-frequency nonlinear energy transfer from linear oscillators to mdof essentially nonlinear attachments

Tsakirtzis

Kerschen

Panagopoulos

et al. 2005

Journal of Sound and Vibration

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We report on multi-frequency energy transfer from a two-mode, initially excited linear system to a multidegree-of-freedom (mdof) essentially nonlinear attachment. This occurs through simultaneous resonance interactions of both linear modes with a set of nonlinear normal modes (NNMs) of the attachment, and is studied utilizing numerical wavelet transforms. The multi-frequency nonlinear energy transfer discussed herein differs from multi-frequency energy transfer caused by resonance capture cascading where sequential energy transfer from a set of linear modes to single-dof nonlinear attachments takes place. r

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Instantaneous Indicators of Structural Behaviour Based on the Continuous Cauchy Wavelet Analysis

Cited by 71 publications

References 4 publications

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Modal parameter identification of a CMUT membrane using response data only

Multi-frequency nonlinear energy transfer from linear oscillators to mdof essentially nonlinear attachments

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