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Research Papers: Seismic Engineering

Modal Techniques for Remote Identification of Nonlinear Reactions at Gap-Supported Tubes Under Turbulent Excitation

[+] Author and Article Information
Xavier Delaune

Laboratoire d’Études de Dynamique, Commissariat à l’Énergie Atomique, CEA, DEN, DM2S, SEMT, F-91191 Gif-sur-Yvette, Francexavier.delaune@cea.fr

José Antunes

Applied Dynamics Laboratory, Instituto Tecnológico e Nuclear, ITN/ADL, Estrada Nacional 10, 2686 Sacavem Codex, Portugaljantunes@itn.pt

Vincent Debut

Applied Dynamics Laboratory, Instituto Tecnológico e Nuclear, ITN/ADL, Estrada Nacional 10, 2686 Sacavem Codex, Portugal

Philippe Piteau, Laurent Borsoi

Laboratoire d’Études de Dynamique, Commissariat à l’Énergie Atomique, CEA, DEN, DM2S, SEMT, F-91191 Gif-sur-Yvette, France

J. Pressure Vessel Technol 132(3), 031801 (May 05, 2010) (11 pages) doi:10.1115/1.4001077 History: Received June 15, 2009; Revised December 16, 2009; Published May 05, 2010

Predictive computation of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation has been the subject of very active research. Nevertheless, experimental results are still very important, for validation of the theoretical predictions as well as for asserting the integrity of field components. Because carefully instrumented test tubes and tube-supports are seldom possible, due to space limitations and to the severe environment conditions, there is a need for robust techniques capable of extracting, from the actual vibratory response data, information that is relevant for asserting the components integrity. The dynamical contact/impact (vibro-impact) forces are of paramount significance, as are the tube/support gaps. Following our previous studies in this area using wave-propagation techniques (De Araújo, Antunes, and Piteau, 1998, “Remote Identification of Impact Forces on Loosely Supported Tubes: Part 1—Basic Theory and Experiments,” J. Sound Vib., 215, pp. 1015–1041; Antunes, Paulino, and Piteau, 1998, “Remote Identification of Impact Forces on Loosely Supported Tubes: Part 2—Complex Vibro-Impact Motions,” J. Sound Vib., 215, pp. 1043–1064; Paulino, Antunes, and Izquierdo, 1999, “Remote Identification of Impact Forces on Loosely Supported Tubes: Analysis of Multi-Supported Systems,” ASME J. Pressure Vessel Technol., 121, pp. 61–70), we apply modal methods in the present paper for extracting such information. The dynamical support forces, as well as the vibratory responses at the support locations, are identified from one or several vibratory response measurements at remote transducers, from which the support gaps can be inferred. As for most inverse problems, the identification results may prove quite sensitive to noise and modeling errors. Therefore, topics discussed in the paper include regularization techniques to mitigate the effects of nonmeasured noise perturbations. In particular, a method is proposed to improve the identification of contact forces at the supports when the system is excited by an unknown distributed turbulence force field. The extensive identification results presented are based on realistic numerical simulations of gap-supported tubes subjected to flow turbulence excitation. We can thus confront the identified dynamical support contact forces and vibratory motions at the gap-support with the actual values stemming from the original nonlinear computations. The important topic of dealing with the imperfect knowledge of the modal parameters used to build the inverted transfer functions is thoroughly addressed elsewhere (Debut, Delaune, and Antunes, 2009, “Identification of Nonlinear Interaction Forces Acting on Continuous Systems Using Remote Measurements of the Vibratory Responses,” Proceedings of the Seventh EUROMECH Solids Mechanics Conference (ESMC2009), Lisbon, Portugal, Sept. 7–11). Nevertheless, identifications are performed in this paper based on both the exact modes and also on randomly perturbed modal parameters. Our results show that, for the system addressed here, deterioration of the identifications is moderate when realistic errors are introduced in the modal parameters. In all cases, the identified results compare reasonably well with the real contact forces and motions at the gap-supports.

Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Configurations used in numerical simulations: beam length L=1 m, support location xC=0.6 m, response measurement locations x1=0.21 m, and x2=0.77 m. (a) First configuration with a symmetrical gap δC=±10−3 m. (b) Second configuration with permanent contact

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Figure 2

Dimensionless equivalent reference spectrum ΦEref(fR) of the turbulence forces per unit tube length, as a function of the reduced frequency fR=fD/V¯f, and the corresponding local excitation turbulence spectrum ΦT(f)

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Figure 3

Tube responses for the gap-support configuration (a)

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Figure 4

Tube responses for the preload configuration (b)

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Figure 5

Response spectra for the gap-support configuration (a)

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Figure 6

Response spectra for the preload configuration (b)

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Figure 7

Transfer functions H(xC,x1,ω) and H(xC,x2,ω) used to compute the impact forces from the acceleration, velocity, and displacement

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Figure 8

Nonregularized impact force identification for the gap-support configuration (a)

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Figure 9

Optimal values of the regularization parameters by minimizing the difference between two estimates of the impact force from the acceleration signals

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Figure 10

Regularized impact force identification for the gap-support configuration (a)

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Figure 11

Regularized identification of the tube motion at the support location for the gap-support configuration (a)

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Figure 12

Regularized impact force identification for preload configuration (b)

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Figure 13

Regularized identification of the tube motion at the support location for preload configuration (b)

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Figure 14

Inverse condition number for the transformation matrices [Ma(ω)], [Mv(ω)], and [Md(ω)]

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Figure 15

Global inverse condition numbers for the transformation matrices [Ma(ω)], [Mv(ω)], and [Md(ω)]

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Figure 16

Turbulence-corrected impact force identification for the gap-support configuration (a)

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Figure 17

Turbulence-corrected identification of the tube motion at the support location for the gap-support configuration (a)

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Figure 18

Turbulence-corrected impact force identification for preload configuration (b)

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Figure 19

Turbulence-corrected identification of the tube motion at the support location for preload configuration (b)

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Figure 20

Random error perturbations applied to the modal parameters used for the identifications

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Figure 21

Effect of random errors in the modal parameters used for the identifications at the gap-support configuration (a). Turbulence-corrected identifications of the impact force and of the tube motion at the support location (identifications performed from the remote acceleration responses).

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Figure 22

Effect of random errors in the modal parameters used for the identifications at the gap-support configuration (b). Turbulence-corrected identifications of the impact force and of the tube motion at the support location (identifications performed from the remote acceleration responses).

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