The problem of statistically bounding the response of an engineering structure with random boundary conditions is addressed across the entire frequency range: from the low, through the mid, to the high frequency region. Extreme-value-based bounding of both the FRF and the energy density response is examined for a rectangular linear plate with harmonic point forcing. The proposed extreme-value (EV) approach, previously tested only in the low frequency region for uncoupled and acoustically-coupled uncertain structures, is examined here in the mid and high frequency regions in addition to testing at low frequencies. EV-based bounding uses an asymptotic threshold exceedance model of Type-I, to extrapolate the m-observational return period to an arbitrarily-large batch of structures. It does this by repeatedly calibrating the threshold model at discrete frequencies using a small sample of response data generated by Monte Carlo simulation or measurement. Here the discrete singular convolution (DSC) method – a transfrequency computation approach for deterministic vibration - is used to generate Monte Carlo samples. The accuracy of the DSC method is first verified (i) in terms of the spatial distribution of total energy density and (ii) across the frequency range, by comparison with a mode superposition method and Statistical Energy Analysis (SEA). EV-based bound extrapolations of the receptance FRF and total energy density are then compared with: (i) directly-estimated bounds using a full set of Monte Carlo simulations and (ii) with total mean energy levels obtained with SEA. This paper shows that for a rectangular plate structure with random boundary conditions, EV-based statistical bounding of both the FRF and total energy density response is generally applicable across the entire frequency range.

References

References
1.
Cotoni
,
V.
,
Shorter
,
P. J.
, and
Langley
,
R. S.
, 2007, “
Numerical and Experimental Validation of a Hybrid Finite Element-Statistical Energy Analysis Method
,”
J. Acoust. Soc. Am.
,
122
(
1
), pp.
259
270
.
2.
Reboul
,
E. S.
,
Le Bot
,
A.
,
Liaudet
,
J. P.
,
Mori
,
M.
, and
Houjoh
,
H.
, 2007, “
A Hybrid Method for Vibroacoustics Based on the Radiative Energy Transfer Method
,”
J. Sound Vib.
,
303
, pp.
675
690
.
3.
Vanmaele
,
C.
,
Vandepitte
,
D.
, and
Desmet
,
W.
, 2007, “
An Efficient Wave Based Prediction Technique for Plate Bending
,”
Comput. Methods Appl. Mech. Eng.
,
196
, pp.
3178
3189
.
4.
Thompson
,
D. J.
,
Fergusson
,
N. S.
,
Yoo
,
J. W.
, and
Rohlfing
,
J.
, 2008, “
Structural Waveguide Behaviour of a Beam–Plate System
,”
J. Sound Vib.
,
318
, pp.
206
226
.
5.
Evans
,
M.
, and
Swartz
,
T.
, 2000,
Aproximating Integrals Via Monte-Carlo and Deterministic Methods
,
Oxford University Press
,
New York.
6.
Hohenbichler
,
M.
, and
Rackwitz
,
R.
, 1988, “
Improvement of Second-Order Reliability Estimates by Importance Sampling
,”
J. Eng. Mech.
,
114
, pp.
2195
2199
.
7.
Dunne
,
L. W.
, and
Dunne
,
J. F.
, 2009, “
An FRF Bounding Methodology for Randomly Uncertain Structures With or Without Coupling to an Acoustic Cavity
,”
J. Sound Vib.
,
322
, pp.
98
134
.
8.
Lin
,
Y. K.
, and
Cai
,
G. Q.
, 1995,
Probabilistic Structural Mechanics
,
McGraw-Hill
,
New York.
9.
Kiureghian
,
A. D.
, and
Ke
,
J.
, 1988, “
The Stochastic Finite Element Method in Structural Reliability
,”
Probab. Eng. Mech.
,
3
, pp.
83
91
.
10.
Melchers
,
R.
, 1999,
Structural Reliability and Prediction
, 2nd ed.,
John Wiley and Sons
,
Chichester, UK
.
11.
Lyon
,
R. H.
, and
DeJong
,
R. G.
, 1998,
Statistical Energy Analysis
, 2nd ed.,
RH Lyon Corp.
,
Cambridge
.
12.
Keane
,
A.
, and
Price
,
W.
, eds., 1997,
Statistical Energy Analysis
,
Cambridge University Press
,
Cambridge
.
13.
Thite
,
A. N.
, and
Mace
,
B. R.
, 2007, “
Robust Estimation of Coupling Loss Factors From Finite Element Analysis
,”
J. Sound Vib.
,
303
, pp.
814
831
.
14.
Yan
,
H.
,
Parrett
,
A.
, and
Nack
,
W.
, 2000, “
Statistical Energy Analysis by Finite Elements for Middle Frequency Vibration
,”
Finite Elem. Anal. Design
,
35
, pp.
297
304
.
15.
Vlahopoulos
,
N.
, and
Zhao
,
X.
, 2001, “
An Investigation of Power Flow in the Mid-Frequency Range for Systems of Co-Linear Beams Based on a Hybrid Finite Element Formulation
,
J. Sound Vib.
,
242
(
3
), pp.
445
473
.
16.
Ji
,
L.
Mace
,
B. R.
, and
Pinnington
,
R. J.
, 2006,
A Mode-Based Approach for the Mid-Frequency Vibration Analysis of Coupled Long- and Short-wavelength Structures
,”
J. Sound Vib.
,
289
, pp.
148
170
.
17.
Peng
,
W.
,
He
,
Z.
,
Li
,
P.
, and
Wang
,
J.
, 2007, “
A Prediction Technique for Dynamic Analysis of Flat Plates in Mid-Frequency Range
,”
Acta Mech. Solida Sinica
,
20
(
4
), pp.
333
341
.
18.
Zhao
,
X.
, and
Vlahopoulos
,
N.
, 2004, “
A Basic Hybrid Finite Element Formulation for Mid-Frequency Analysis of Beams Connected at an Arbitrary Angle
,”
J. Sound Vib.
,
269
, pp.
135
164
.
19.
Coles
,
S.
, 2001,
An Introduction to Statistical Modelling of Extreme-Values
,
Springer-Verlag
,
London
.
20.
Wei
,
G. W.
,
Zhao
,
Y. B.
, and
Xiang
,
Y.
, 2002, “
A Novel Approach for the Analysis of High Frequency Vibrations
,”
J. Sound Vib.
,
257
(
2
), pp.
207
246
.
21.
Seçgin
,
A.
, and
Sarigül
,
A. S.
, 2009, “
A Novel Scheme for the Discrete Prediction of High-Frequency Vibration Response: Discrete Singular Convolution-Mode Superposition Approach
,”
J. Sound Vib.
,
320
, pp.
1004
1022
.
22.
Seçgin
,
A.
,
Dunne
,
J. F.
, and
Zoghaib
,
L.
, 2010, “
Transfrequency FRF Bounding of Uncertain Plate Structures Using Extreme Value Theory and Discrete Singular Convolution
,”
ECCM 2010 - IV European Conference on Structural Mechanics - Solids, Structures and Coupled Problems in Engineering
, Paris, May 16–21.
23.
Hasofer
,
A. M.
1996, “
Non-Parametric Estimation of Failure Probabilities
,”
Mathematical Models for Structural Reliability Analysis, Mathematical Modelling Series
,
Casciati
,
F.
, and
Roberts
,
J. B.
, eds.,
CRC Press
,
Boca Raton
, pp.
195
226
.
24.
Weissman
,
I.
, 1978, “
Estimation of Parameters and Large Quantiles Based on the k Largest Observations
,”
J. Am. Stat. Assoc.
,
73
(
364
), pp.
812
815
.
25.
Hasofer
,
A. M.
, and
Wang
,
J. Z.
, 1992, “
A Test for Extreme Value Domain of Attraction
,”
J. Am. Stat. Assoc.
,
87
(
417
), pp.
171
177
.
26.
Fahy
,
F. J.
, and
Mohammed
,
A. D.
, 1992, “
A Study of Uncertainty in Applications of SEA to Coupled Beam and Plate Systems, Part I: Computational Experiments
,”
J. Sound Vib.
,
158
(
1
), pp.
45
67
.
27.
Gur
,
Y.
,
Wagner
,
D. A.
, and
Morman
,
K. N.
, 1999, “
Energy Finite Element Analysis Methods for Mid-Frequency NVH Applications
,”
Noise and Vibration Conference
,
SAE
, pp.
1159
1167
.
28.
Rabbiolo
,
G.
,
Bernhard
,
R. J.
, and
Milner
,
F. A.
, 2004, “
Definition of a High-Frequency Threshold for Plates and Acoustical Spaces
,”
J. Sound Vib.
,
277
, pp.
647
667
.
You do not currently have access to this content.