Engineering Transactions, Online first
10.24423/engtrans.3493.2025

Comparative Study of Matrix Methods for Modeling the Dispersive Character of Ultrasonic Guided Waves

Ismaine ZITOUNI
ORCID ID 0000-0002-3538-2761
Natioanl High School of Electricity and Mecahnics
Morocco

Hassan RHIMINI
ORCID ID 0000-0002-5784-9844
Natioanl High School of Electricity and Mecahnics
Morocco

Abdelkerim CHOUAF
ORCID ID 0000-0003-1765-6762
Natioanl High School of Electricity and Mecahnics
Morocco

This paper presents a comparative study of various matrix methods for obtaining the dispersion curves of ultrasonic guided waves in anisotropic media for both planar and cylindrical geometries. First, the mathematical formulation of the problem is introduced. Then, matrix methods are employed to generate the characteristic dispersion functions, with a particular focus on multilayer structures. To simplify the problem and enhance convergence, the formulation of Lamb modes is separated from that of shear modes. Dispersion curves are then plotted for single and multilayer planar and cylindrical geometries of propagating modes, with each case identifying the different modes obtained and explaining their symmetry characteristics. The dispersion curves are generated using a MATLAB program and compared with two software tools: Disperse Calculator for plates and GUIGUW for cylindrical structures. A perfect match is observed.

A discussion is then presented to highlight the advantages and limitations of the matrix methods, offering reliable insights into which matrix method is most suitable for each type of waveguide and enabling the plotting of convergent curves with minimal computation time.

Keywords: guided waves; dispersion curves; composite; laminate; matrix method; pipeline
Full Text: PDF
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).

References

Yao D., Zheng J., Jin L., Meng X., Zhan Z., Fan R., Ming P., Effect of surface oxidation on the interfacial and mechanical properties in graphite/epoxy composites composite bipolar plates, Chinese Chemical Letters, 35(11): 109382, 2023, https://doi.org/10.1016/j.cclet.2023.109382.

Boushab D., Ouidadi H., Mote A., Priddy M., Kundu S., Pittman Jr C.U., Grunlan, J., Wang Q., Lacy Jr T., Fire impact on mechanically failed graphite/epoxy composites, Polymer Composites, 44(4): 2236–2249, 2023, https://doi.org/10.1002/pc.27239.

Nayfeh A.H., The general problem of elastic wave propagation in multilayered anisotropic media, The Journal of the Acoustical Society of America, 89(4): 1521–1531, 1991, https://doi.org/10.1121/1.400988.

Nayfeh A.H., The propagation of horizontally polarized shear waves in multilayered anisotropic media, The Journal of the Acoustical Society of America, 86(5): 2007–2012, 1989, https://doi.org/10.1121/1.398580.

Datta S.K., Physical ultrasonics of composites, The Journal of the Acoustical Society of America, 130(6): 4170–4171, 2011, https://doi.org/10.1121/1.3655882.

Kamal A.M., Gresil M., Giurgiutiu V., Comparative study of several methods for the calculation of ultrasonic guided waves in composites, [in:] 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, American Institute of Aeronautics and Astronautics, April 8–11, 2013, Boston, MA, 2013, https://doi.org/10.2514/6.2013-1901.

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

Monnier T., Lamb waves-based impact damage monitoring of a stiffened aircraft panel using piezoelectric transducers, Journal of Intelligent Material Systems and Structures, 17(5): 411–421, 2006, https://doi.org/10.1177/1045389X06058630.

Azkour M., El Allami M., Rhimini H., Calculation of the dispersion curves modeling the propagation of ultrasonic Lamb waves in a bonded aluminum/epoxy/aluminum structure using the semi-analytical finite element method, Engineering Transactions, 72(2): 119–143, 2024, https://doi.org/10.24423/EngTrans.3171.2024.

Yacoubi A., Jabiri A., Azkour M., Mandry R., El Allami M., Wavelet analysis of ultrasonic Lamb wave displacements in three-layer adhesive plates: continuous wavelet transform (CWT) versus the semi-analytical element method (SAFEM), Engineering Transactions, 72(2): 203–224, 2024, https://doi.org/10.24423/EngTrans.3207.2024.

Zitouni I., Rhimini H., Chouaf A., Comparative study of the spectral method, DISPERSE and other‎ classical methods for plotting the dispersion curves in‎ anisotropic plates, Journal of Applied and Computational Mechanics, 9(4): 955–973, 2023, https://doi.org/10.22055/jacm.2023.42530.3941.

Zitouni I., Rhimini H., Chouaf A., Modeling the propagation of ultrasonic guided waves in a composite plate by a spectral approximation method, Engineering Transactions, 71(2): 213–227, 2023, https://doi.org/10.24423/EngTrans.3073.20230510.

Zitouni I., Mekkaoui M., Rhimini H., Chouaf A., Innovative approach to modeling propagative, non-propagative and complex modes of ultrasonic guided waves, Mechanics of Advanced Materials and Structures, 1–14, 2024, https://doi.org/10.1080/15376494.2024.2370032.

Liu H., Huang Z., Yin Z., Sun M., Bo L., Li T., Tian Z., Investigation of viscoelastic guided wave properties in anisotropic laminated composites using a Legendre orthogonal polynomials expansion−assisted viscoelastodynamic model, Polymers, 16(12): 1638, 2024, https://doi.org/10.3390/polym16121638.

Bocchini P., Marzani A., Viola E., Graphical user interface for guided acoustic waves, Journal of Computing in Civil Engineering, 25(3): 202–210, 2011, https://doi.org/10.1061/(ASCE)CP.1943-5487.00000.

Huber A., The dispersion calculator – a free software for calculating dispersion curves of guided waves, [in:] 20th World Conference on Non-Destructive Testing (WCNDT 2024), Incheon, South Korea, 2024, https://doi.org/10.58286/29894.

Barski M., Pająk P., Determination of dispersion curves for composite materials with the use of stiffness matrix method, Acta Mechanica et Automatica, 11(2), 2017, https://doi.org/10.1515/ama-2017-0019.

Zitouni I., Rhimini H., Chouaf A., A combined Newton–bisection approach for calculating the dispersion curves in anisotropic multilayered waveguides, Journal of Vibration Engineering & Technologies, 12(2): 5189–5201, 2024, https://doi.org/10.1007/s42417-023-01191-1.

Zitouni I., Rhimini H., Chouaf A., Modeling the propagation of ultrasonic guided waves in four-layer laminated composites, [in:] Azari Z., El Had K., Ait Ali M.E., El Mahi A., Chaari F., Haddar M. [Eds.] Advances in Applied Mechanics. JET 2022. Lecture Notes in Mechanical Engineering, Springer, Cham, 2024, https://doi.org/10.1007/978-3-031-49727-8_3.

Zitouni I., Rhimini H., Chouaf A., Calculation of dispersion curves in the composite graphite-epoxy plate by a hybrid analytic method, [in:] Advances in Mechanics. CMM 2022. Lecture Notes in Mechanical Engineering, Aniss S., et al. [Eds.], Springer, Cham, 2024, https://doi.org/10.1007/978-3-031-46973-2_1.

Zitouni I., Rhimini H., Chouaf A., Spectral method for modeling the dispersion of complex guided wave modes in anisotropic pipeline, Journal of Computational Applied Mechanics, 55(3): 473–484, 2024, https://doi.org/10.22059/jcamech.2024.376537.1090.




DOI: 10.24423/engtrans.3493.2025