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Research Papers

Detection of Nonlinearities in Plates Via Higher-Order-Spectra: Numerical and Experimental Studies

[+] Author and Article Information
M. Pasquali

Department of Mechanical and
Aerospace Engineering,
Sapienza University,
Rome 00184, Italy

W. Lacarbonara

Mem. ASME
Associate Professor
Department of Structural and
Geotechnical Engineering,
Sapienza University,
Rome 00184, Italy

P. Marzocca

Mem. ASME
Professor
Department of Mechanical and
Aeronautical Engineering,
Clarkson University,
Potsdam, NY 13699
e-mail: pmarzocc@clarkson.edu

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received March 20, 2013; final manuscript received May 5, 2014; published online June 2, 2014. Assoc. Editor: Bogdan I. Epureanu.

J. Vib. Acoust 136(4), 041015 (Jun 02, 2014) (13 pages) Paper No: VIB-13-1082; doi: 10.1115/1.4027625 History: Received March 20, 2013; Revised May 05, 2014

Higher-order spectral (HOS) analysis tools are employed to extract the nonlinear dynamic response features of elastic and laminated plates by using both physics-based mechanical plate models and experimental data. Bispectral and trispectral densities are computed to highlight the presence and relative importance of quadratic and cubic nonlinearities. The former are associated with the presence of asymmetry either in the excitation or in the mechanical response of predeflected plates while the latter are due to midplane stretching effects. Besides the detection of these structural nonlinearities in perfect (baseline) fully clamped plates, the changes of such nonlinearities induced by the presence of small inertial imperfections (i.e., lumped masses) are identified and exploited to localize the imperfections. The numerical and experimental investigations are carried out both on isotropic and laminated composite plates subject to Gaussian white noise excitation. The effectiveness of the HOS-based procedure for detection of the nonlinearities is fully demonstrated for both types of plates.

Copyright © 2014 by ASME
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References

Figures

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Fig. 1

Schematic of the experimental layout of the plate and its clamping apparatus. Reprinted with permission [13]. Copyright 2011 Elsevier.

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Fig. 2

Schematic of the plate under investigation. Points R, A, B, and C represent the positions where the random excitation is applied, and where the added mass is located, respectively.

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Fig. 3

The experimental layout of tests

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Fig. 4

Geometry of the stress-free plate (configuration Bo) and deformed material lines through ro(xα) spanning the base plane. The current position of material points of the base plane is po(xα) = ro(xα)+uo(xα) where uo(xα) is the displacement vector. Reprinted with permission [13]. Copyright 2011 Elsevier.

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Fig. 5

The response of a fully clamped squared aluminum plate specimen (span = 254 mm, thickness = 0.813 mm) to an increasing central point load at A. The midpoint deflections predicted by the nonlinear theory (solid line) and by Mindlin– Reissner (straight line) theories are compared with the experimental measurements (dots). Reprinted with permission [13]. Copyright 2011 Elsevier.

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Fig. 6

(Left) Linear mode shapes of the spring-steel plate obtained using the AF-ESPI method [22] (first column, reprinted with permission [22]), the theoretical plate model (second and third columns) and the PSV-400 laser scanner vibrometer (last column) for the steel plate

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Fig. 7

Linear mode shapes of the Graphil 34-600 laminated plate obtained using the theoretical model (first and second columns) and the PSV-400 vibrometer (last column) for the laminated plate

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Fig. 8

The lowest four mode shapes of the baseline (first column) and modified (second and third columns) steel plates. Similar results are obtained using the composite plate as specimen.

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Fig. 9

Experimental time history of (a) the applied force and (c) the plate response at A together with the (b) input power spectrum normalized with respect to the frequency (in log scale) and (d) the power spectrum of the response (the latter is estimated acquiring the system response in correspondence of the left-upper clamped corner of the plate, so as to guarantee the best output in terms of clarity of the related FFT)

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Fig. 10

Experimentally obtained bispectra for the steel plate: (a) baseline, (b) lumped mass at A (Test 1), (c) lumped mass at B (Test 2), and (d) doubled lumped mass at B (Test 3)

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Fig. 11

The power spectrum of the system response acquired at the left-upper corner of the steel plate when it has a mass at its center and a mass at A and is subject to a GWN

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Fig. 12

Numerically obtained bispectra for the modified steel plate (additional mass at its center): (a) baseline, (b) lumped mass at A (Test 1), (c) lumped mass at B (Test 2), and (d) doubled lumped mass at B (Test 3)

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Fig. 13

The experimental (first and third columns) and numerical (second and fourth columns) contour plots of the bispectrum-based nonlinearity index for the steel plate (first and second columns) and for the laminated plate (third and fourth columns) for Test 1, Test 2, and Test 3. The red circle and the black cross indicate the mass actual position and that of the ID(2) peak, respectively.

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Fig. 14

The experimental (first and third columns) and numerical (second and fourth columns) contour plots of the trispectrum-based nonlinearity index for the steel plate (first and second columns) and for the laminated plate (third and fourth columns) for Test 1, Test 2, and Test 3. The red circle and the black cross indicate the position and that of the ID(3) peak, respectively.

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Fig. 15

The numerically obtained contour plot of the trispectrum-based nonlinearity index for the steel plate with the mass at C

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