Modeling the Propagation of Ultrasonic Guided Waves in a Composite Plate by a Spectral Approximation Method

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Authors

  • Ismaine ZITOUNI Hassan II University, Morocco
  • Hassan RHIMINI Hassan II University, Morocco
  • Abdelkerim CHOUAF Hassan II University, Morocco

Abstract

Graphite-epoxy composites have been able to meet the multiple requirements of the space industry. However, the radiation from the spatial environment and non-perfect adhesion between the fibers and the matrix can lead to the appearance of imperfections. To handle this, we use non-destructive testing by ultrasonic guided waves known for its high accuracy in detecting defects. In this article, we study the propagation of ultrasonic guided waves in a graphite-epoxy composite plate by the spectral method. First, the mathematical formalism is explained for modeling guided waves in the composite material. Next, we plot the dispersion curves of the composite plate in different orientations of the fibers with a MATLAB program and the results are compared with those of the DISPERSE software. These give us information on the modes that propagate in the structure. We elaborate and explain a technique based on displacement symmetry to distinguish between the different modes. A discussion based on time-saving and accuracy is established to show the advantages of the method.

The second part of our paper consists in giving a physical meaning to the spectral displacements normalized in amplitude. We propose to normalize the spectral eigenvectors by the acoustic power. We plot the displacement and stress profiles of the guided modes and we compare our results to the analytical ones. Perfect correspondence is found, indicating the accuracy of the approach developed. In addition, a study of the vibrational state in the composite plate is established for Lamb and horizontal shear modes at a specific frequency.

Keywords:

guided waves, spectral method, dispersion curves, graphite-epoxy composite, acoustic power, normalized displacement

References

1. Lee D.G., Suh N.P., Axiomatic Design and Fabrication of Composite Structures: Applications in Robots, Machine Tools, and Automobiles, Oxford University Press, New Yok 2005.

2. Lukez R., The use of graphite/epoxy composite structures in space applications, 1st Annual USU Conference on Small Satellites, 1987.

3. Harb M.S., Yuan F.G., Non-contact ultrasonic technique for Lamb wave characterization in composite plates, Ultrasonics, 64: 162–169, 2016, https://doi.org/10.1016/j.ultras.2015.08.011

4. Katz T., Mackiewicz S., Ranachowski Z., Kowalewski Z.L., Antolik Ł., Ultrasonic detection of transversal cracks in rail heads–theoretical approach, Engineering Transactions, 69(4): 437–456, 2021, https://doi.org/10.24423/EngTrans.1695.20211220

5. Matsuo T., Hatanaka D., Development of non-contact fatigue crack propagation monitoring method using air-coupled acoustic emission system, Engineering Transactions, 67(2): 185–198, 2019, https://doi.org/10.24423/EngTrans.1009.20190405

6. Guo S., Rebillat M., Mechbal N., Dichotomy property of dispersion equation of guided waves propagating in anisotropic composite plates, Mechanical Systems and Signal Processing, 164: 108212, 2022, https://doi.org/10.1016/j.ymssp.2021.108212

7. Ndiaye E.B., Duflo H., Non destructive testing of sandwich composites: adhesion defects evaluation; experimental and finite element method simulation comparison, [In:] Proceedings of the Acoustics 2012 Nantes Conference, April 23-27, 2012, Nantes, France, pp. 2659–2664.

8. Rokhlin S.T., Chimenti D.E., Nagy P.B., Physical Ultrasonics of Composites, Oxford Academic Press, 2011, https://doi.org/10.1093/oso/9780195079609.001.0001

9. Yu J.G., Zhang B., Lefebvre J.E., Zhang C.H., Wave propagation in functionally graded piezoelectric rods with rectangular cross-section, Archives of Mechanics, 67(3): 213–231, 2015.

10. Zhang X.M., Yu J.G., Effects of initial stresses on guided waves in unidirectional plates, Archives of Mechanics, 65(1): 3–26, 2013.

11. Zhang X., Liang S., Shao S., Yu J., A quadrature-free Legendre polynomial approach for the fast modelling guided circumferential wave in anisotropic fractional order viscoelastic hollow cylinders, Archives of Mechanics, 73(2): 121–152, 2021, https://doi.org/10.24423/aom.3642

12. Barazanchy D., Giurgiutiu V., A comparative convergence and accuracy study of composite guided-ultrasonic wave solution methods: Comparing the unified analytic method, SAFE method and DISPERSE, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231(16): 2961–2973, 2017, https://doi.org/10.1177/0954406217700928

13. Hebaz S.E., Benmeddour F., Moulin E., Assaad J., Semi-analytical discontinuous Galerkin finite element method for the calculation of dispersion properties of guided waves in plates, The Journal of the Acoustical Society of America, 143(1): 460–469, 2018, https://doi.org/10.1121/1.5021588

14. Adamou A.T.I., Craster R.V., Spectral methods for modelling guided waves in elastic media, The Journal of the Acoustical Society of America, 116(3): 1524–1535, 2004, https://doi.org/10.1121/1.1777871

15. Karpfinger F., Gurevich B., Bakulin A., Modeling of wave dispersion along cylindrical structures using the spectral method, The Journal of the Acoustical Society of America, 124(2): 859–865, 2008, https://doi.org/10.1121/1.2940577

16. Quintanilla F.H., Lowe M.J.S., Craster R.V., Modeling guided elastic waves in generally anisotropic media using a spectral collocation method, The Journal of the Acoustical Society of America, 137(3): 1180–1194, 2015, https://doi.org/10.1121/1.4913777

17. Pavlakovic B., Lowe M., Alleyne D., Cawley P., Disperse: A general purpose program for creating dispersion curves, [In:] Thompson D.O., Chimenti D.E. [Eds] Review of Progress in Quantitative Nondestructive Evaluation, vol 16, pp. 185–192, Springer, Boston, MA, 1997, https://doi.org/10.1007/978-1-4615-5947-4_24

18. Weideman J.A., Reddy S.C., A MATLAB differentiation matrix suite, ACM Transactions on Mathematical Software (TOMS), 26(4): 465–519, 2000, https://doi.org/10.1145/365723.365727

19. Nayfeh A.H., Wave Propagation in Layered Anisotropic Media: with Application to Composites, Elsevier, 1995.

20. Rhimini H., El Allami M., Sidki M., Haddout A., Benhadou M., Ultrasonic guided waves in tri-layer structure. Application to study the interaction of guided waves with hidden defect at low frequency, Technical Acoustics (Техническая акустика), 16: 1–14, 2016.

21. Hernandez-Crespo B., Engineer B., Courtney C., Empirical technique for dispersion curve creation for guided wave applications. [In:] 8th European Workshop on Structural Health Monitoring, July 5–8, 2016 in Bilbao, Spain, pp. 1375–1384, e-Journal of Nondestructive Testing, 21(8), https://www.ndt.net/?id=19911

22. Mori N., Biwa S., Transmission characteristics of the S0 and A0 Lamb waves at contacting edges of plates, Ultrasonics, 81: 93–99, 2017, https://doi.org/10.1016/j.ultras.2017.06.009

23. Benmeddour F., Grondel S., Assaad J., Moulin E., Experimental study of the A0 and S0 Lamb waves interaction with symmetrical notches, Ultrasonics, 49(2): 202–205, 2009, https://doi.org/10.1016/j.ultras.2008.08.002