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Research Papers

Variability Analysis of Modal Characteristics of Frequency-Dependent Visco-Elastic Three-Layered Sandwich Beams With Spatial Random Geometrical and Material Properties

[+] Author and Article Information
Frédéric Druesne

Laboratoire Roberval UMR CNRS 7337,
Centre de Recherche de Royallieu,
Université de Technologie de Compiègne,
CS 60319,
Compiègne Cedex 60203, France
e-mail: frederic.druesne@utc.fr

Mohamed Hamdaoui, El Mostafa Daya

LEM3 UMR 7239,
Université de Lorraine,
Ile du Saulcy,
Metz Cedex 01 57045, France

Qi Yin

Laboratoire Roberval UMR CNRS 7337,
Centre de Recherche de Royallieu,
Université de Technologie de Compiègne,
CS 60319,
Compiègne Cedex 60203, France

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received February 8, 2017; final manuscript received May 17, 2017; published online August 1, 2017. Assoc. Editor: Mohammed Daqaq.

J. Vib. Acoust 139(6), 061007 (Aug 01, 2017) (10 pages) Paper No: VIB-17-1049; doi: 10.1115/1.4036930 History: Received February 08, 2017; Revised May 17, 2017

Material and physical properties of a frequency-dependent visco-elastic sandwich beam are modeled as a set of spatial random fields and represented by means of the Karhunen–Loève expansion. Variability analysis of frequency and loss factor are performed. An efficient approach based on modal stability procedure (MSP) is used, the so-called Monte Carlo simulation (MCS)–MSP method. The latter provides very reliable results and allows to analyze the impact of the input variability of a high number of random spatial quantities on the output response. The effect of independent and correlated couples of spatial random fields is investigated. It is shown that the output variability is generally more important for damping than for natural frequencies. Moreover, it is demonstrated that the input variability in geometrical properties are the most impacting for damping and frequency. The influence of input coefficient of variation on output variability is also studied. It is shown that a negative correlation between the face and core thicknesses result in high levels of output variability, when one parameter increases as the other decreases.

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References

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Figures

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Fig. 1

Sandwich beam's configuration

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Fig. 2

Relative error (%)—MSP mesh convergence for first mode , second mode , third mode , fourth mode , fifth mode , and sixth mode : (a) frequencies and (b) loss factors

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Fig. 3

One trial of random field G0(x,θ) with input CoV(G0) = 5% for different correlation lengths 0.001L, 0.01L, 0.1L, 1L, 10L, 100L, and nominal value: (a) midpoint method and (b) local average method

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Fig. 4

Variability of frequency ···· and loss factor for first mode , second mode , third mode , fourth mode , fifth mode , and sixth mode : (a) input CoV(G0) = 5%, (b) input CoV(ρc) = 5%, (c) input CoV(δj) = 5%, and (d) input CoV(Ωj) = 5%

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Fig. 5

Variability of frequency ···· and loss factor for first mode , second mode , third mode , fourth mode , fifth mode , and sixth mode : (a) input CoV(Ef) = 5% and (b) input CoV(ρf) = 5%

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Fig. 6

Variability of frequency ···· and loss factor for first mode , second mode , third mode , fourth mode , fifth mode , and sixth mode : (a) input CoV(hf) = 5% and (b) input CoV(hc) = 5%

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Fig. 7

Influence of stochastic parameters coupling on output CoV with correlation length 1L and input CoV = 5%

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Fig. 8

Output CoV of frequency ···· and loss factor with different correlation coefficient between thicknesses hf and hc for first mode , second mode , third mode , fourth mode , fifth mode , and sixth mode : (a) input CoV(hf,hc) = 5% and (b) input CoV(hf,hc) = 15%

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Fig. 9

Mean frequency response function's ···· and 95% confidence interval for the displacement in the middle of the beam with correlation coefficient between thicknesses hf and hc equal to−1: (a) input CoV(hf,hc) = 5% and (b) input CoV(hf,hc) = 15%

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Fig. 10

Distribution of first frequency and loss factor with correlation length 1L for input CoV(core parameters) 1%, 5%, 10%, 15%, 20%, and 25%: (a) frequencies and (b) loss factors

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Fig. 11

Influence of input coefficient of variation on output statistic quantities of first frequency ···· and loss factor : (a) adimensional mean and (b) output CoV

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