This paper presents initial results from a program to develop a “rapid screening test” for determining the in-plane fiber distributions in unidirectionally reinforced composite structures by the use of the vibration response measurements and Galerkin’s method. Theoretical models and experimental data are generated on the basis of two methods: (1) the “shifting method,” in which the effective length of the beam is changed, and (2) the “added mass method”, in which the mass distribution of the beam is changed. The elastic constants and the density are all assumed to be functions of fiber volume fraction, while the spatial distribution of the fiber volume fraction is assumed to be given by a polynomial function. The concept of an effective density is employed to obtain the appropriate solution to the coefficients of the polynomial function. Results show that the fundamental mode gives rise to better predictions of physical properties than the higher modes do. An error analysis includes discussion of the errors due to the influences of the mode number, the assumed order of the polynomial in the fiber volume fraction distribution, and the bending-extension coupling effect caused by the unsymmetrical distribution of properties about the beam middle surface.

1.
Ayorinde
 
E. O.
, and
Gibson
 
R. F.
,
1993
, “
Elastic Constants of Orthotropic Composite Materials Using Plate Resonant Frequencies, Classical Lamination Theory and an Optimized Three-Mode Rayleigh Formulation
,”
Composites Engineering
, Vol.
3
, No.
5
, pp.
395
407
.
2.
Barcilon
 
V.
,
1976
, “
Inverse Problem for a Vibrating Beam
,”
Journal of Applied Mathematics and Physics (ZAMP)
, Vol.
27
, pp.
347
357
.
3.
Barcilon
 
V.
,
1982
, “
Inverse Problem for the Vibrating Beam in the Free-Clamped Configuration
,”
Royal Society of London, Philosophical Transactions
, Vol.
A304
, pp.
211
251
.
4.
Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Van Nostrand Reinhold, New York.
5.
Chen, W. H., 1995, “Determination of Property Distributions of Nonuniform Composites by the Use of Vibration Measurements,” Ph.D. dissertation, Wayne State University, Detroit, MI.
6.
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
.
7.
DeWilde, W. P., 1984, “Determination of the Material Constants of an Anisotropic Lamina by Free Vibration Analysis,” Proceedings of the 2nd International Modal Analysis Conference, Orlando, FL, 1, pp. 44–49.
8.
Gibson, R. F., Hwang, S. J., and Chen, W. H., 1992, “Vibration Response Measurements for Determination of Physical Property Distributions in Laminated Composite Beams,” Proceedings of the 8th ASM/ESD Advanced Composites Conference, Chicago, IL, Nov. 2–5, ASM International Materials, Park, OH, pp. 317–326.
9.
Gladwell, G. M. L., 1986, Inverse Problems in Vibration, Martinus Nijhoff, Dordrecht, The Netherlands.
10.
Gladwell
 
G. M. L.
,
1987
, “
Examples of Reconstruction of an Euler-Bernoulli Beam from Spectral Data
,”
Journal of Sound and Vibration
, Vol.
119
, No.
1
, pp.
81
94
.
11.
Hensel, E., 1991, Inverse Theory and Applications for Engineers, Prentice-Hall, Englewood Cliffs, NJ.
12.
Laura
 
P. A. A.
,
Pombo
 
J. L.
, and
Susemihl
 
E. A.
,
1974
, “
A Note on the Vibrations of a Clamped-Free Beam with a Mass at the Free End
,”
Journal of Sound and Vibration
, Vol.
37
, No.
2
, pp.
161
168
.
13.
Nelson, M. F., and Wolf, J. A., 1992, “A Nondestructive Technique for Determining the Elastic Constants of Advanced Composites,” Vibro-Acoustic Characterization of Materials and Structures, ASME, P. K. Raju, ed., ASME, New York, pp. 227–233.
14.
Stokes
 
V. K.
,
1990
, “
Random Glass Mat Reinforced Thermoplastic Composites, Part I: Phenomenology of Tensile Modulus Variations
,”
Polymer Composites
, Vol.
11
, pp.
32
44
.
15.
Suarez
 
S. A.
, and
Gibson
 
R. F.
,
1987
, “
Improved Impulse-Frequency Response Techniques for Measurement of Dynamic Mechanical Properties of Composite Materials
,”
Journal of Testing and Evaluation
, Vol.
15
, No.
2
, pp.
114
121
.
16.
Tung, R. W., 1987, “Effect of Processing Variables on the Mechanical and Thermal Properties of Sheet Molding Compound,” Short Fiber Reinforced Composite Materials, ASTM STP 772, B. A. Sanders, ed., American Society for Testing and Materials, Philadelphia, PA, pp. 51–63.
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