Determining Elastic Constants of Material Using Optimization Method and Vibration Test

Abstract:

This paper proposes an inverse method to obtain the elastic properties of material. The sum of the squared differences between the experimental resonance frequencies and calculated resonance frequencies from the finite element method is chosen as the objective function. The proposed method presents an optimization method, Hybrid Genetic /Simulated Annealing algorithm, to determine the elastic properties. When the objective function reaches its minimum value, its corresponding design variables are the elastic constants of the material. The inverse method is applied to determine the elastic constants of aluminum plate, Glass/PP laminate, and double coated steel plate .The results indicate that for few elastic constants as an aluminum plate, Hybrid Genetic /Simulated Annealing algorithm has no apparent improvement, but more calculation time in comparison method. While simulated annealing while for Glass/PP laminate and double coated steel plate with more elastic constants, Hybrid Genetic /Simulated Annealing algorithm is superior to the traditional simulated annealing method.

• Periodical: Materials Science Forum (Volumes 628-629)
• Pages: 89-96
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.628-629.89
• Online since: August 2009
• Authors: Yu Hua Lin, Chia Lung Chang
• Keywords: Elastic Property, Hybrid Genetic /Simulated Annealing Algorithm, Vibration Test

References

[1] F. Forster, Ein neues Messverfahren zur Bestimmung des Elastizitats-moduls und der Dampfung, Zeitschrift fuer Metallkunde 29 (1937) 109-115.

[2] H. Sol, Identification of anisotropic plate rigidities using free vibrationdata, PhD Thesis, Vrije Universiteit, Brussel, Belgium, (1986).

[3] P.W. De Wilde, H. Sol, Anisotropic material identification using measured resonant frequencies of rectangular composite plates, Fourth International Conference on Composite Structures, Paisley College of Technology, Scotland, 1987, pp.2317-2324.

DOI: 10.1007/978-94-009-3457-3_24

[4] H. Sol, H. Hua, J. De Visscher, J. Vantomme, W.P. De Wilde, A mixed numerical/experimental technique for the nondestructive identification of the stiffness properties of fiber reinforced composite materials, Journal of NDT&E International 30 (2) (1997).

DOI: 10.1016/s0963-8695(96)00049-7

[5] E.O. Ayorinde, R.F. Gibson, Elastic constants of orthotropic composite materials using plate resonance frequencies, classical lamination theory and an optimized three mode Rayleigh formulation, Composite Engineering 3 (1993) 395-407.

DOI: 10.1016/0961-9526(93)90077-w

[6] F. Moussu, M. Nivoit, Determination of the elastic constants of orthotropic plates by a modal analysis method of superposition, Journal of Sound and Vibration 165 (1993) 149-163.

DOI: 10.1006/jsvi.1993.1248

[7] W.P. De Wilde, B. Narmon, H. Sol, M. Roovers, Determination of the material constants of an anisotropic lamina by free vibration an analysis, in: Proceedings of the Second International Modal Analysis Conference, Orlando, FL, 1984, pp.44-49.

[8] L.R. Deobald, R.F. Gibson, Determination of elastic constants of orthotropic plates by modal analysis/Rayleigh-Ritz technique, Journal of Sound and Vibration 124 (1988) 269-283.

DOI: 10.1016/s0022-460x(88)80187-1

[9] P. Pedersen, P.S. Frederiksen, Identification of orthotropic material modules by a combined experimental/numerical method, Measurement 10 (1992) 113-118.

DOI: 10.1016/0263-2241(92)90003-m

[10] M.E. McIntyre, J. Woodhouse, On measuring the elastic and damping constants of orthotropic sheet materials, Acta Metallurgica 36 (1988) 1397-1416.

DOI: 10.1016/0001-6160(88)90209-x

[11] K.E. Fallstrom, M.A. Jonsson, A nondestructive method to determine material properties in anisotropic plates, Polymer Composites 12 (1991) 293-305.

DOI: 10.1002/pc.750120502

[12] S.F. Hwang, C.S. Chang, Determination of elastic constants of materials by vibration testing, Composite Structures 49 (2000) 183-190.

DOI: 10.1016/s0263-8223(99)00132-4

[13] P. Pedersen, Optimisation method applied to identification of materials parameters, in: H.A. Eschenauer,G. Thierau(Eds. ), Discretization Methods and Structural Optimisation-Procedures and Applications, Springer, Berlin, 1989, pp.277-283.

DOI: 10.1007/978-3-642-83707-4_35

[14] C.M. Mota Soares, M. Moreira de Freitas, A.L. Araujo, P. Pedersen, Identification of material properties of composite plate specimens, Composite Structures 25 (1993) 277-285.

DOI: 10.1016/0263-8223(93)90174-o

[15] R. Rikards, A. Chate, W. Steinchen, A. Kessler, A.K. Bledzki, Method for identification of elastic properties of laminates based on experiment design, Composites Part B 30 (1999) 279-289.

DOI: 10.1016/s1359-8368(98)00059-6

[16] C. Maletta, L. Pagnotta, Determining material properties in anisotropic plates using genetic algorithms and vibration test data, International Journal of Mechanics and Materials in Design 1 (2004) 199-211.

[17] T. Lauwagie , H. Sol , W. Heylen , G. Roebben , Determination of the in-plane elastic properties of the different layers of laminated plates by means of vibration testing and model updating , Jouranl of Sound and Vibration (2004) 529-546.

DOI: 10.1016/j.jsv.2003.05.023

[18] T. Lauwagie , Konstantina Lambrinou, Sophoclis Patsias, Ward Heylen, Jef Vleugels , Resonant-based identification of the elastic properties of layered materials: Application to air-plasma sprayed thermal barrier coatings , NDT&E International 41 (2008).

DOI: 10.1016/j.ndteint.2007.08.007

[19] Marco Alfano , Leonardo Pagnotta , Determining the elastic constants of isotropic materials by modal vibration testing of rectangular thin plates , Journal of Sound and Vibration(2006) 426-439.

DOI: 10.1016/j.jsv.2005.10.021

[20] Joel Cugnoni , Thomas Gmur , Alain Schorderet , Inverse method based on modal analysis for characterizing the constitutive properties of thick composite plates , Computer & Structures 85(2007) 1310-1320.

DOI: 10.1016/j.compstruc.2006.08.090

[21] G. B. Warburton , The vibration of rectangular plates , Proceedings of the Institution of Mechanical Engineers 168 (1953) 371-384.