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.

References

References
1.
Boubaker
,
M. B.
,
Druesne
,
F.
,
Lardeur
,
P.
,
Barillon
,
F.
, and
Mordillat
,
P.
,
2012
, “
Uncertain Vibration Analysis of an Automotive Car Body Modeled by Finite Elements With the Modal Stability Procedure
,”
International Conference on Noise and Vibration Engineering (ISMA) and International Conference on Uncertainty in Structural Dynamics (USD)
, Leuven, Belgium, Sept. 17–19, pp. 4489–4502.
2.
Mourelatos
,
Z. P.
,
Majcher
,
M.
, and
Geroulas
,
V.
,
2016
, “
Time-Dependent Reliability Analysis of Vibratory Systems With Random Parameters
,”
ASME J. Vib. Acoust.
,
138
(
3
), p.
031007
.
3.
Guedri
,
M.
,
de Lima
,
A. M. G.
,
Bouhaddi
,
N.
, and
Rade
,
D. A.
,
2010
, “
Robust Design of Visco-Elastic Structures Based on Stochastic Finite Element Models
,”
Mech. Syst. Signal Process.
,
24
(
1
), pp.
59
77
.
4.
Dey
,
S.
,
Mukhopadhyay
,
T.
, and
Adhikari
,
S.
,
2015
, “
Stochastic Free Vibration Analyses of Composite Shallow Doubly Curved Shells: A Kriging Model Approach
,”
Composites, Part B
,
70
(
1
), pp.
99
112
.
5.
de Lima
,
A. M. G.
,
da Silva
,
A. R.
,
Rade
,
D. A.
, and
Bouhaddi
,
N.
,
2010
, “
Component Mode Synthesis Combining Robust Enriched Ritz Approach for Viscoelastically Damped Structures
,”
Eng. Struct.
,
32
(
5
), pp.
1479
1488
.
6.
Arnoult
,
E.
,
Lardeur
,
P.
, and
Martini
,
L.
,
2011
, “
The Modal Stability Procedure for Dynamic and Linear Finite Element Analysis With Variability
,”
Finite Elem. Anal. Des.
,
47
(
1
), pp.
30
45
.
7.
Druesne
,
F.
,
Boubaker
,
M. B.
, and
Lardeur
,
P.
,
2014
, “
Fast Methods Based on Modal Stability Procedure to Evaluate Natural Frequency Variability for Industrial Shell-Type Structures
,”
Finite Elem. Anal. Des.
,
89
, pp.
93
106
.
8.
Hamdaoui
,
M.
,
Druesne
,
F.
, and
Daya
,
E. M.
,
2015
, “
Variability Analysis of Frequency Dependent Visco-Elastic Three-Layered Beams
,”
Compos. Struct.
,
131
, pp.
238
247
.
9.
Rao
,
D. K.
,
1978
, “
Frequency and Loss Factors of Sandwich Beams Under Various Boundary Conditions
,”
J. Mech. Eng. Sci.
,
20
(
5
), pp.
271
282
.
10.
Bilasse
,
M.
,
Daya
,
E. M.
, and
Azrar
,
L.
,
2010
, “
Linear and Nonlinear Vibrations Analysis of Viscoelastic Sandwich Beams
,”
J. Sound Vib.
,
329
(
23
), pp.
4950
4969
.
11.
Koutsawa
,
Y.
,
Charpentier
,
I.
,
Daya
,
E. M.
, and
Cherkaoui
,
M.
,
2008
, “
A Generic Approach for the Solution of Nonlinear Residual Equations—Part I: The Diamant Toolbox
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
3–4
), pp.
572
577
.
12.
Hamdaoui
,
M.
,
Robin
,
G.
,
Jrad
,
M.
, and
Daya
,
E. M.
,
2015
, “
Optimal Design of Frequency Dependent Three-Layered Rectangular Composite Beams for Low Mass and High Damping
,”
Compos. Struct.
,
120
, pp.
174
182
.
13.
Zhu
,
W. Q.
,
Ren
,
Y. J.
, and
Wu
,
W. Q.
,
1992
, “
Stochastic FEM Based on Local Averages of Random Vector Fields
,”
J. Eng. Mech.
,
118
(
3
), pp.
496
511
.
14.
Yin
,
Q.
,
Druesne
,
F.
, and
Lardeur
,
P.
,
2016
, “
The CGSM for Static Analysis of Multilayered Composite Plates With Variability of Material and Physical Properties
,”
Compos. Struct.
,
140
, pp.
360
368
.
15.
Ghanem
,
G. R.
, and
Spanos
,
D. P.
,
1991
,
Stochastic Finite Elements: A Spectral Approach
,
Springer-Verlag
,
New York
.
16.
Karhunen
,
K.
,
1946
, “
Zur spektral theorie stochastischer prozesse
,”
Annales Academiae Scientiarum Fennicae
, Vol.
37
, Academia Scientiarum Fennica, Mariankatu, Finland.
17.
Trindade
,
M. A.
,
Benjeddou
,
A.
, and
Ohayon
,
R.
,
2000
, “
Modeling of Frequency-Dependent Viscoelastic Materials for Active-Passive Vibration Damping
,”
ASME J. Vib. Acoust.
,
122
(
2
), pp.
169
174
.
18.
Ewins
,
D. J.
,
1984
,
Modal Testing: Theory and Practice
,
Research Studies Press
,
Baldock, Hertfordshire, UK
.
19.
Hernández
,
W. P.
,
Castello
,
D. A.
, and
Ritto
,
T. G.
,
2016
, “
Uncertainty Propagation Analysis in Laminated Structures With Viscoelastic Core
,”
Comput. Struct.
,
164
, pp.
23
37
.
20.
Druesne
,
F.
,
Hamdaoui
,
M.
,
Lardeur
,
P.
, and
Daya
,
E. M.
,
2016
, “
Variability of Dynamic Responses of Frequency Dependent Visco-Elastic Sandwich Beams With Material and Physical Properties Modeled by Spatial Random Fields
,”
Compos. Struct.
,
152
, pp.
316
323
.
21.
Noh
,
H. C.
, and
Lee
,
P. S.
,
2007
, “
Higher Order Weighted Integral Stochastic Finite Element Method and Simplified First-Order Application
,”
Int. J. Solids Struct.
,
44
(11–12), pp.
4120
4144
.
22.
Druesne
,
F.
,
Hallal
,
J.
,
Lardeur
,
P.
, and
Lanfranchi
,
V.
,
2016
, “
Modal Stability Procedure Applied to Variability in Vibration From Electromagnetic Origin for an Electric Motor
,”
Finite Elem. Anal. Des.
,
122
, pp.
61
74
.
You do not currently have access to this content.