This paper relates a further development of an earlier work by the authors, in which they presented a method for deriving the four independent elastic constants (longitudinal and transverse Young’s moduli, in-plane shear modulus and major Poisson’s ratio) of an orthotropic material from resonance data obtained in a modal analysis of a freely-supported plate made out of the material. In the present work, simple averaging, as opposed to the weighted averaging employed in the earlier version, is utilized. The use of three modes and six modes is compared on the basis of results of both the forward and the inverse problems. Results are obtained for materials spanning orthotropy ratios from unity (i.e., isotropic) to about 13. The results suggest that, in comparison with our earlier method, the improved method is easier to use and is just as accurate. The adaptability of the basic method developed by the authors to various levels and types of refinement is also demonstrated, as is the potential of the method for fast characterization of elastic properties of advanced composites.

1.
American Society for Testing and Materials, 1987, ASTM Standards and Literature References for Composite Materials, ASTM, Philadelphia, PA.
2.
Automotive Composites Consortium, 1990, Test Procedures for Automotive Structural Composite Materials, A.C.C., Troy, MI.
3.
Ayorinde, E. O., and Gibson, R. F., 1992, “Optimized Six-mode Rayleigh Formulation for Determination of Elastic Constants of Orthotropic Composite Materials from Plate Vibration Resonance Data,” Vibroacoustic Characterization of Materials & Structures, NCA-Vol. 14, P. K. Raju, ed., American Society of Mechanical Engineers, New York, pp. 167–175.
4.
Ayorinde, E. O., 1993, “Determining Elastic Constants of Orthotropic Composite Plates Using an Optimized Rayleigh Formulation Including Through-the-thickness Shear and Rotary Inertia,” Dynamic Characterization of Advanced Materials, NCA-Vol. 16, AMD-Vol 172, P. K. Raju and R. F. Gibson, eds., American Society of Mechanical Engineers, New York, pp. 77–85.
5.
Ayorinde
E. O.
, and
Gibson
R. F.
,
1993
, “
Elastic Constants of Orthotropic Composite Materials Using Plate Resonance Frequencies, Classical Lamination Theory and an Optimized Three-mode Rayleigh Formulation
,”
Composites Engineering
, Vol.
3
, No.
5
, pp.
395
407
.
6.
Ayorinde, E. O., Gibson, R. F., and Wen, Y. F., 1993, “Elastic Constants of Isotropic and Orthotropic Composite Materials from Plate Vibration Test Data,” Composite Materials: Testing and Design (Eleventh Volume), ASTM STP 1206, E. T. Camponeschi, Jr., ed., American Society for Testing and Materials, Philadelphia, pp. 150–161.
7.
Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold Company, New York, NY, pp. 261–264.
8.
Deobald
L. R.
, and
Gibson
R. F.
,
1988
, “
Determination of Elastic Constants of Orthotropic Plates by a Modal Analysis/Rayleigh-Ritz Technique
,”
Journal of Sound and Vibration
, Vol.
124
, No.
2
, pp.
269
283
.
9.
Jones, R. M., 1975, Mechanics of Composite Materials, Hemisphere Publishing Corporation, New York.
10.
Kim
C. S.
, and
Dickinson
S. M.
,
1985
, “
Improved Approximate Expressions for the Natural Frequencies of Isotropic and Orthotropic Rectangular Plates
,”
Journal of Sound and Vibration
, Vol.
103
, No.
1
, pp.
142
149
.
11.
Leissa
A. W.
,
1973
, “
The Free Vibration of Rectangular Plates
,”
Journal of Sound and Vibration
, Vol.
31
, No.
3
, pp.
257
293
.
12.
Strutt, J. W. S., (Lord Rayleigh), 1945, Chapter VIII, Theory of Sound, Second Edition, Dover, New York.
13.
Sullivan, J. L., 1991, Private Communication, Ford Motor Company, Dearborn, MI.
14.
Warburton
G. B.
,
1954
, “
The Vibration of Rectangular Plates
,”
Proceedings of the Institution of Mechanical Engineers
, Vol.
168
, pp.
371
374
.
This content is only available via PDF.
You do not currently have access to this content.