This paper presents a theoretical approach for identifying the dimensionless mean coefficient of participating fuzzy mass which is the main unknown parameter of the type I or II fuzzy law previously introduced by the author. This method is based on the use of the associated power flow equation, each power term being identified by using a global statistical energy analysis of the fuzzy structure (master structure with its fuzzy substructures). Identification is then carried out by solving a nonlinear constrained optimization problem. An example is given to illustrate the theoretical results.

1.
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
, (English edition). Vol.
5
, pp.
49
67
.
2.
Cuschieri
J. M.
, and
Feit
D.
,
1995
, “
Acoustic Scattering from a Fluid-Loaded Elastic Plate with a Distributed Inhomogeneity of Varying Length Scales
,”
J. Acoust. Soc. Am.
, Vol.
98
, No.
5
, pp.
2889
2889
.
3.
Dyer
I.
,
1994
, “
Scattering from Internally Complex Finite Shell Models
,”
J. Acoust. Soc. Am.
, Vol.
95
, No.
5
, pp.
2867
2867
.
4.
Feit
D.
, and
Pierce
A. D.
,
1995
, “
Vibrations and Acoustical Response of Fuzzy Structures
,”
J. Acoust. Soc. Am.
, Vol.
97
, No.
1
, pp.
705
705
.
5.
Grace, A., 1992, Optimization Toolbox for Use with Matlab, The Math Works Inc., Natick, MA.
6.
Lyon
R. H.
,
1995
,
Statistical Energy Analysis and Structural Fuzzy
,
J. Acoust. Soc. Am.
, Vol.
97
, No.
5
, pp.
2878
2881
.
7.
Lyon, R. H., and DeJong, R. G., 1995, Theory and Application of Statistical Energy Analysis, Butterworth-Heinemann.
8.
Maidanik
G.
,
1995
, “
Power Dissipation in a Sprung Mass Attached to a Master Structure
,”
J. Acoust. Soc. Am.
, Vol.
98
, No.
6
, pp.
3527
3533
.
9.
Maidanik
G.
, and
Dickey
J.
,
1995
, “
An Impulse Response Function for a Fuzzy Structure
,”
J. Acoust. Soc. Am.
, Vol.
97
, No.
3
, pp.
1460
1476
.
10.
McCoy
J. J.
,
1994
, “
The Theory of Fuzzy Structures—A Statistical Continuum Mechanics Interpretation
,”
J. Acoust. Soc. Am.
, Vol.
95
, No.
5
, pp.
2846
2846
.
11.
Pierce
A. D.
,
1994
, “
Mass Per Unit Natural Frequency as a Descriptor of Internal Fuzzy Structure
,”
J. Acoust. Soc. Am.
, Vol.
95
, No.
5
, pp.
2845
2845
.
12.
Pierce, A. D., 1995a, “Resonant-Frequency-Distribution of Internal Mass Inferred from Mechanical Impedance Matrices,” Proceedings of the ASME 15th Biennal Conference on Mechanical Vibration and Noise, ASME, Boston, MA, pp. 229–239.
13.
Pierce
A. D.
,
1995
b, “
Fuzzy Elements, their Coupling Rules, and the Jaynes-Shannon Maximum Entropy Principle
,”
J. Acoust. Soc. Am.
, Vol.
98
, No.
5
, pp.
2946
2946
.
1.
Pierce, A. D., Sparrow, V. W., and Russell, D. A., 1993, “Fundamental Structural-Acoustic Idealizations for Structures with Fuzzy Internals,” Paper 93-WA/NCA-17, ASME Winter Annual Meeting, New Orleans, LA, Nov. 28–Dec. 3.
2.
and also in JOURNAL OF VIBRATION AND ACOUSTICS, Vol. 117, pp. 339–348, 1995.
1.
Photiadis
D. M.
,
1995
, “
Scattering from Complex Elastic Structures
,”
J. Acoust. Soc. Am.
, Vol.
98
, No.
5
, pp.
2963
2963
.
2.
Rochat
J. L.
, and
Sparrow
V. W.
,
1994
, “
The Effects of Fuzzy Attachments on Compressional and Shear Waves in a Plate
,”
J. Acoust. Soc. Am.
, Vol.
95
, No.
5
, pp.
2847
2847
.
3.
Rochat, J. L., and Sparrow, V. W., 1995, “Incorporating Compressional and Shear Wave Types into Fuzzy Structure Models Plates,” Proceedings of the ASME 15th Biennal Conference on Mechanical Vibration and Noise, ASME, Boston, MA, pp. 247–252.
4.
Ruckman, C. E., and Feit, D., 1995a, “Fuzzy Structural Analysis: A Simple Example,” Proceedings of the 15th International Congress on Acoustics, M. Newman ed., lUPAP, Trondheim, Norway.
5.
Ruckman, C. E., and Feit, D., 1995b, “Tutorial on Soize’s Method for Stochastic Modeling in Structural Acoustics (Fuzzy Structure Analysis),” Proceedings of the ASME 15th Biennal Conference on Mechanical Vibration and Noise, ASME, Boston, MA, pp. 241–246.
6.
Russell, D. A., 1995, “The Theory of Fuzzy Structures and its Application to Waves in Plates and Shells,” Ph.D. Thesis. The Pennsylvania State University, Graduate Program in Acoustics, State College, Pennsylvania.
7.
Russell
D. A.
, and
Sparrow
V. W.
,
1992
, “
Acoustic Scattering from a Fluid-Loaded Plate With an Attached Structural Fuzzy
,”
J. Acoust. Soc. Am.
, Vol.
91
, pp.
2440
2440
.
8.
Russell
D. A.
, and
Sparrow
V. W.
,
1995
, “
Backscattering from a Baffled Finite Plate Strip with Fuzzy Attachments
,”
J. Acoust. Soc. Am.
, Vol.
98
, No.
3
, pp.
1527
1533
.
9.
Soize
C.
,
1986
, “
Probabilistic Structural Modeling in Linear Dynamic Analysis of Complex Mechanical Systems. I—Theoretical Elements
,”
La Recherche Ae´rospatiale
, (English edition). Vol.
5
, pp.
23
48
.
10.
Soize
C.
,
1993
, “
A Model and Numerical Method in the Medium Frequency Range for Vibroacoustic Predictions Using the Theory of Structural Fuzzy
,”
J. Acoust. Soc. Am.
, Vol.
94
, No.
2
, pp.
849
865
.
11.
Soize
C.
,
1995
, “
Vibration Damping in Low-Frequency Range Due to Structural Complexity. A Model Based on the Theory of Fuzzy Structures and Model Parameters Estimation
,”
Computers and Structures
, Vol.
58
, No.
5
, pp.
901
915
.
12.
Soize
C.
,
Desanti
A.
, and
David
J. M.
,
1992
, “
Numerical Methods in Elastoacoustics for Low and Medium Frequency Ranges
,”
La Recherche Ae´rospatiale
, (English edition). Vol.
5
, pp.
25
44
.
13.
Sparrow
V. W.
,
1991
, “
Soize’s Theory of Structural Fuzzy: An Examination of Fundamental Assumptions
,”
J. Acoust. Soc. Am.
, Vol.
89
, pp.
1867
1867
.
14.
Sparrow
V. W.
,
1995
, “
Time Domain Simulation and Visualization of Fuzzy Structures
,”
J. Acoust. Soc. Am.
, Vol.
98
, No.
5
, Pt. 2, pp.
2947
2947
.
15.
Sparrow
V. W.
,
Russell
D. A.
, and
Rochat
J. L.
,
1994
, “
Implementation of Discrete Fuzzy Structure Models in Mathematica
,”
International Journal for Numerical Methods in Engineering
, Vol.
37
, pp.
3005
3014
.
16.
Steinberg
B. Z.
, and
McCoy
J. J.
,
1995
, “
Towards Local Effective Parameter Theories Using Multiresolution Decomposition
,”
J. Acoust. Soc, Am.
, Vol.
96
, No.
2
, pp.
1130
1143
.
17.
Strasberg, M., 1996, “Continuous Structures as ’Fuzzy’ Substructures,” J. Acoust. Soc. Am., (in press).
18.
Strasberg
M.
, and
Feit
D.
,
1996
, “
Vibration Damping of Large Structures Induced by Attached Small Resonant Structures
,”
J. Acoust. Soc. Am.
, Vol.
99
, No.
1
, pp.
335
344
.
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