Sage Journals: Discover world-class research

Abstract

A method for determination of orthotropic elastic material properties of plates using resonance frequencies is developed and verified. The elastic properties are found through minimization of the difference between experimentally measured resonance frequencies and the eigenfrequencies obtained by finite element (FE) analysis using the plate stiffnesses as parameters. Mindlin type plate theory is used. Emphasis is on the practical use of knowledge about uncertainties to compute bounds of the obtained stiffnesses. Variations of the optimization problem formulation incorporating the known uncertainties, combined with a suitable scalar stiffness norm, enables the calculation of the upper and lower bounds of the stiffnesses. Further, an advantage with the present (FE-based) method is that more complex plate shapes can be analyzed than for similar methods based on Rayleigh-Ritz displacement field assumptions. This is verified with good results on orthotropic composite laminates using specimen geometries including comer singularities. The method is successfully validated against another, but similar, vibration technique.

Keywords

composite testing orthotropic stiffness experimental modal finite element uncertainties comer singularity

Get full access to this article

View all access options for this article.

References

1. Christensen, R. M. 1991. Mechanics of Composite Materials, Lawrence Livermore Laboratory, University of California, Livermore, Malabar, FL: Krieger Publishing Company.

2. Kuttenkeuler, J. and U. Ringertz . 1997. "Aeroelastic Design Optimization with Experimental Verification," Report 96-33, NFFP Project 254, Dept. of Aeronautics, Royal Institute of Technology.

3. Kuttenkeuler, J. and U. Ringertz . 1997. "Aeroelastic Tailoring Considering Uncertainties in Material Properties," NFFP Project 254, Dept. of Aeronautics, Royal Institute of Technology.

4. Curtis, P. T. 1988. "CRAG Test Methods for the Measurement of the Engineering Properties of Fibre Reinforced Plastics," Technical Report 88012, Fanborough, Great Britain: Royal Aerospace Establishment.

5. ASTM . 1991. Annual Book of ASTM Standards, Philadelphia, PA: American Society for Testing and Materials.

6. Gommers, B. , I. Verpoest and P. Van Houtte . 1996. "Further Developments in Testing and Analysis of the Plate Twist Test for In-Plane Shear Modulus Measurements," J. of Composites, Part A27A.

7. Frederiksen, P. S. 1992. "Identification of Material Parameters in Anisotropic Plates A Combined Numerical/Experimental Method," DCAMM Report S 60, Dept. of Solid Mechanics, The Technical University of Denmark.

8. Frederiksen, P. S. 1997. "Experimental Procedure and Results for the Identification of Elastic Constants of Thick Orthotropic Plates," Journal of Composite Materials, 31(4).

9. Deobald, L. R. and R. F. Gibson . 1988. "Determination of Elastic Constants of Orthotropic Plates by a Modal Analysis/Rayleigh-Ritz Technique," Journal of Sound and Vibration, 124(2):269-283.

10.

10. Fällström, K. E. 1991. "Determining Material Properties in Anisotropic Plates Using Rayleigh's Method," Journal of Polymer Composites, 12(5).

11.

11. Sol, H. , J. Visscher and J. Vantomme . "Measurement of Complex Moduli of Composite Materials and Discussion of Some Results," Proc. European Mech. Coll., 269, Elsevier, London, pp. 16-29.

12.

12. Engrand, D. and D. Louis . 1979. "Identification of the Elastic Characteristics of Composite Materials by Means of Vibration Tests and Model of Discrete Conservative Calculations," Recherche Aerospatiale, 6:401-410.

13.

13. Nelson, M. F. and J. A. Wolf 1992. "A Nondestructive Technique for Determining the Elastic Constants of Advanced Composites," Vibro-Acoustic Characterization of Materials and Structures, NCA-Vol.14, ASME, pp. 227-233.

14.

14. Sol, H. 1990. "Identification of Complex Moduli of Composite Materials by a Mixed Numerical-Experimental Method," Proceedings of the 9th International Conference on Experimental Mechanics, Copenhagen: Askegaad, Asby Tryk, 2:562-571.

15.

15. Johnson, G. W. 1994. Lab View Graphical Programming: Practical Applications in Instrumentation and Control, McGraw-Hill, Inc.

16.

16. Ewings, D. J. 1994. Modal Testing. Theory and Practice. University of Sussex, England, Research Studies Press Ltd., Taunton, Somerset, England.

17.

17. Szabó, B. and I. Babuska . 1991. Finite Element Analysis, John Wiley & Sons, Inc.

18.

18. Hughes, T. J. R. and M. Cohen . 1978. "The Heterosis Finite Element for Plate Bending," Computers and Structures, 9:445-450.

19.

19. Maschhoff, K. J. and D. C. Sorensen . 1996. "A Portable Implementation of ARPACK for Distributed Memory Parallel Architectures," Copper Mountain Conference on Iterative Methods.

20.

20. Thomson, W. 1981. Theory of Vibration with Applications, 2nd Edition, Dept. of Mechanical and Environmental Engineering, University of California, Prentice-Hall, Inc., Englewood Cliffs.

21.

21. Gill, P. E. , W. Murray and M. H. Wright . 1993. Practical Optimization. Academic Press Ltd., San Diego.

22.

22. Larsson, D. 1997. "Using Modal Analysis For Estimation of Anisotropic Material Constants," Journal of Engineering Mechanics, 123(3):222-229.

23.

23. The Math Works Inc. 1992. "MATLAB(r) High Performance Numeric Computation and Visualization Software," Reference Guide, Prentice-Hall, Inc. NJ.

24.

24. Svanberg, K. 1993. "The Method of Moving Asymptotes (MMA) with Some Extensions," Optimization of Large Structural Systems, Kluwer, Dordrecht, The Nethrlands, 1:555-566.

A Finite Element Based Modal Method for Determination of Plate Stiffnesses Considering Uncertainties

Abstract

Keywords

Get full access to this article

References