Fundamental issues relative to structural vibration and to scattering of sound from structures with imprecisely known internals are explored, with the master structure taken as a rectangular plate in a rigid baffle, which faces an unbounded fluid medium on the external side. On the internal side is a fuzzy structure, consisting of a random array of point-attached spring-mass systems. The theory predicts that the fuzzy internal structure can be approximated by a statistical average in which the only relevant property is a function mF(Ω) which gives a smoothed-out total mass, per unit plate area, of all those attached oscillators which have their natural frequencies less than a given value Ω. The theory also predicts that the exact value of the damping in the fuzzy structure is of little importance, because the structure, even in the limit of zero damping, actually absorbs energy with an apparent frequency-dependent damping constant proportional to dmF(W)/dω incorporated into the dynamical description of the master structure. A small finite value of damping within the internals will cause little appreciable change to this limiting value.

1.
Achenbach
J. D.
,
Bjarnason
J.
, and
Igusa
T.
,
1992
. “
Effect of a Vibrating Substructure on Acoustic Radiation from a Cylindrical Shell
,”
ASME JOURNAL OF VIBRATION AND ACOUSTICS
, Vol.
114
, pp.
312
318
.
2.
Bender, C. M., and Orszag, S. A., 1978, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, New York, pp. 343–347.
3.
Bjarnason
J.
,
Achenbach
J. D.
, and
Igusa
T.
,
1992
, “
Acoustic Radiation from a Cylindrical Shell with an Internal Plate
,”
Wave Motion
, Vol.
15
, pp.
23
41
.
4.
Chabas
F.
,
Desanti
A.
, and
Soize
C.
,
1986
, “
Probabilistic Structural Modeling in Linear Dynamic Analysis of Complex Mechanical Systems: II. Numerical Analysis and Applications
,”
La Recherche Ae´rospatiale
, Vol.
1986-5
, pp.
49
67
.
5.
Dowell
E. H.
, and
Y. Kubota
Y.
,
1985
. “
Asymptotic Modal Analysis and Statistical Energy Analysis of Dynamical Systems
,”
ASME Journal of Applied Mechanics
, Vol.
52
, pp.
949
957
.
6.
Felsen
L. B.
, and
Guo
Y. P.
,
1991
. “
Hybrid Ray-Mode Parametrization of Acoustic Scattering from Submerged Internally Loaded Thin Cylindrical Elastic Shells: Reformulation of Angular Harmonic Resonant Mode Data
,”
Journal of the Acoustical Society of America
, Vol.
90
, p.
2342
2342
.
7.
Guo
Y. P.
,
1992
, “
Sound Scattering from an Internally Loaded Cylindrical Shell
,”
Journal of the Acoustical Society of America
, Vol.
91
, pp.
926
938
.
8.
Guo
Y. P.
,
1993
. “
Sound Scattering from Cylindrical Shells with Internal Elastic Plates
,”
Journal of the Acoustical Society of America
, Vol.
93
, pp.
1936
1946
.
9.
Huang
H.
,
1979
a. “
Transient Response of Two Fluid-Coupled Spherical Elastic Shells to an Incident Pressure Pulse
,”
Journal of the Acoustical Society of America
, Vol.
65
, pp.
881
887
.
10.
Huang
H.
,
1979
b, “
Transient Response of Two Fluid-Coupled Cylindrical Elastic Shells to an Incident Pressure Pulse
,”
ASME Journal of Applied Mechanics
, Vol.
46
, pp.
513
518
.
11.
Igusa
T.
, and
Tang
Y.
,
1992
. “
Mobilities of Periodic Structures in Terms of Asymptotic Modal Properties
,”
AIAA Journal
, Vol.
30
, pp.
2520
2525
.
12.
Piere, A. D., 1989. Acoustics: An Introduction to Its Physical Principles and Applications, Acoustical Society of America.
13.
Skudrzyk, E., 1968. Simple and Complex Vibratory Systems, Pennsylvania State University Press, State College, Chapter 11.
14.
Skudrzyk
E.
,
1980
, “
The Mean-Value Method of Predicting the Dynamic Response of Complex Vibrators
,”
Journal of the Acoustical Society of America
, Vol.
67
, pp.
1105
1135
.
15.
Soize
C.
,
1986
. “
Probabilistic Structural Modeling in Linear Dynamic Analysis of Complex Mechanical Systems: I. Theoretical Elements
,”
La Recherche Ae´rospatiale
, Vol.
1986-5
, pp.
23
48
.
16.
Soize
C.
,
1993
. “
A Model and Numerical Method in the Medium Frequency Range for Vibroacoustic Predictions Using the Theory of Structural Fuzzy
,”
Journal of the Acoustical Society of America
, Vol.
94
, pp.
849
865
.
17.
Soize
C.
,
Hutin
P. M.
,
Desanti
A.
,
David
J. M.
, and
Chabas
F.
,
1986
. “
Linear Dynamic Analysis of Mechanical Systems in the Medium Frequency Range
,”
Computers and Structures
, Vol.
23
, pp.
605
637
.
18.
Xu
K.
, and
Igusa
T.
,
1992
. “
Dynamic Characteristics of Multiple Substructures with Closely Spaced Frequencies
,”
Earthquake Engineering and Structural Dynamics
, Vol.
21
, pp.
1059
1070
.
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