Modeling propagation of laser–ultrasonic probing pulse in stratified medium by the method of ABCD matrices

The modern methods of modeling acoustic wave travel in stratified media are reviewed, and the necessity of a new and faster technique is justified. The method of modeling elastic wave propagation based on signal conditioning using ABCD matrices and a Python soft ware is described. The theoretical framework and the mathematical algorithm of the presented method are discussed. The main calculations of the main physical and mathematical relations of the method implementation in the program are given. The model signal is correlated with the test signal obtained from a medium with pre-set parameters. The temporal shapes and spectra of the signal inside an optical-acoustic converter are presented for two cases. In the first case, the optical–acoustic converter has a free surface (boundary with air); in the second case, the optical–acoustic converter is pressed to a steel plate. Based on the obtained data, the applicability of the method to modeling acoustic signal propagation in flat and stratified medium is proved. The critical advantage of the proposed modeling approach is high calculating speed of the signal shape and spectrum at any point of the medium and at any assigned time.

Keywords: laser optics–acoustics, ultrasonic control, stratified media, defectoscopy, modeling methods, ABCD matrices, structurescopy, acoustic pulse propagation.
For citation:

Pashkin A. I., Vinnikov V.A. Modeling propagation of laser–ultrasonic probing pulse in stratified medium by the method of ABCD matrices. MIAB. Mining Inf. Anal. Bull. 2020;(6):140-150. [In Russ]. DOI: 10.25018/0236-1493-2020-6-0-140-150.

Issue number: 6
Year: 2020
Page number: 140-150
ISBN: 0236-1493
UDK: 550.3
DOI: 10.25018/0236-1493-2020-6-0-140-150
Article receipt date: 24.03.2020
Date of review receipt: 09.04.2020
Date of the editorial board′s decision on the article′s publishing: 20.05.2020
About authors:

A.I. Pashkin1, Engineer, e-mail:,
V.A. Vinnikov1, Dr. Sci. (Phys. Mathem.), Assistant Professor, Head of Chair, e-mail:,
1 National University of Science and Technology «MISiS», 119049, Moscow, Russia.

For contacts:

V.A. Vinnikov, e-mail:


1. Nazarov V. G. Improvement of imaging quality in computer tomography using special integral transform. Komp'yuternye issledovaniya i modelirovanie. 2015, vol. 7, no 5, pp. 1033— 1046. [In Russ].

2. Dem'yanov A.Yu., Dinariev O.Yu., Lisitsyn D.A. Modeling frequency dependence of dielectric permeability and electrical conductance of saturated porous media. Komp'yuternye issledovaniya i modelirovanie. 2016, vol. 8, no 5, pp. 765—773. [In Russ].

3. Dem'yanov A.Yu., Dinariev O.Yu., Lisitsyn D.A. Method to calculate electrical properties of saturated rocks with regard to surface conductance. Komp'yuternye issledovaniya i modelirovanie. 2015, vol. 7, no 5, pp. 1081—1088. [In Russ].

4. Vavilov V. P. Teplovidenie i teplovoy kontrol' dlya inzhenerov [Thermal imaging and heat control for engineers], Moscow, Spektr, 2017, 72 p.

5. Bychkov A. S., Zarubin V. P., Karabutov A.A., Simonova V.A., Cherepetskaya E. B. On the use of an optoacoustic and laser ultrasonic imaging system for assessing peripheral intravenous access. Photoacoustics. 2017. Vol. 5. Pp. 10—16.

6. Karabutov A.A., Podymova N. B., Cherepetskaya E. B. Measuring the dependence of the local Young's modulus on the porosity of isotropic composite materials by a pulsed acoustic method using a laser source of ultrasound. Journal of Applied Mechanics and Technical Physics, 2013. Vol. 54. No 3. Pp. 500—507.

7. Kravcov A., Shibaev I.A., Blokhin D. I., Krapivnoi M. M., Zarubin V. P. Examination of structural members of aerial vehicles by laser ultrasonic structuroscopy. International Journal of Civil Engineering and Technology. 2018. Vol. 9. No 11. Pp. 2258—2265.

8. Bychkov A., Siminova V., Zarubin V., Cherepetskaya E., Karabutov A. The progress in photoacoustic and laser ultrasonic tomographic imaging for biomedicine and industry. A review. Applied Sciences (Switzerland). 2018. Vol. 8. No 10.

9. Takahashi S., Kobayashi S., Tomas I., Dupre L., Vertesy G. Comparison of magnetic nondestructive methods applied for inspection of steel degradation. NDT & E International. 2017. Vol. 91. Pp. 54—60.

10. Velicheti D., Nagy P. B., Hassan W. Inversion procedure for dual-mode electromagnetic nondestructive characterization of shot-peened IN718. NDT & E International. 2019. Vol. 101. Pp. 17—28.

11. Mottershead J. E., Friswell M. I. Model updating in structural dynamics: a survey. Journal of Sound and Vibration. 1993. Vol. 167. Pp. 347—375. DOI: 10.1006/jsvi.1993.1340.

12. Friswell M. I., Mottershead J. E. Finite element model updating in structural dynamics. Kluwer Academic Publishers, Dordrecht, The Netherlands. 1995. 286 p.

13. Zou Y., Tong L., Steven G. P. Vibration-based model-dependent damage (delamination) identification and health monitoring for composite structures — a review. Journal of Sound and Vibration. 2000. Vol. 230. No 2. Pp. 357—378. DOI: 10.1006/jsvi.1999.2624.

14. Sinha J. K., Friswell M. I., Edqards S. Simplified models for the location of cracks in beam structures using measured vibration data. Journal of Sound and Vibration. 2002. Vol. 251. Pp. 13—38.

15. Liu G. R., Han X. Computational inverse techniques in nondestructive evaluation. CRC Press, Boca Raton, FL. 2003. 592 p.

16. Taheri H., Koester L. W., Bigelow T.A., Bond L. J. Thermoelastic finite element modeling of laser generated ultrasound in additive manufacturing materials. ASNT Annual Conference 2017. Pp. 188—198.

17. Favorskaya A. V. Laser ultrasonic investigation of properties of a plate material through the analysis of multiple waves. Komp'yuternye issledovaniya i modelirovanie. 2019, vol. 11, no 4, pp. 653—673. [In Russ].

18. Sun H., Waisman H., Betti R. A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers. International Journal for Numerical Methods in Engineering. 2015. Vol. 105. No 13. Pp. 1014—1040.

19. Gravenkamp H., Natarajan S., Dornisch W. On the use of NURBS-based discretizations in the scaled boundary finite element method for wave propagation problems. Computer Methods in Applied Mechanics and Engineering. 2017. Vol. 315. Pp. 867—880.

20. Jung J., Jeong C., Taciroglu E. Identification of a scatterer embedded in elastic heterogeneous media using dynamic XFEM. Computer Methods in Applied Mechanics and Engineering. 2013. Vol. 259. Pp. 50—63.

21. Zvelto O. Printsipy lazerov [Principles of lasers], Saint-Petersburg, Lan', 2008, 720 p.

22. Gerrard A., Burch J. Introduction to matrix methods in optics. London: Wiley, 1975. 384 p.

23. Gusev V. E., Karabutov A.A. Lazernaya optoakustika [Laser opto-acoustics], Moscow, Nauka, 1991, 304 p.

24. Vinogradova M. B., Rudenko O. V., Sukhorukov A. P. Teoriya voln [Theory of waves], Moscow, Nauka, 1979, 432 p.

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