eesti teaduste
akadeemia kirjastus
SINCE 1952
Proceeding cover
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2020): 1.045
Simulation of solitary wave propagation in carbon fibre reinforced polymer; pp. 297–303
PDF | doi: 10.3176/proc.2015.3.14

Martin Lints, Andrus Salupere, Serge Dos Santos

The emergence and propagation of solitary waves is investigated for carbon fibre reinforced polymer using numerical simulations for Non-Destructive Testing (NDT) purposes. The simulations are done with the Chebyshev collocation method. The simplest laminate model is used for the periodical structure of the material from which dispersion will arise. Classical and nonclassical nonlinearities are introduced in the constitutive equation. The balance of the dispersion and nonlinearity is analysed by studying the shape-changing effects of the medium on the initial input pulse and the possibility of solitary wave propagation is considered. Future applications of solitary waves for nonlinear medical imaging and NDT of materials are discussed.


  1. Dos Santos, S. and Prevorovsky, Z. Imaging of human tooth using ultrasound based chirp-coded nonlinear time reversal acoustics. Ultrasonics, 2011, 51, 667–674.

  2. Frazier, M., Taddese, B., Antonsen, T., and Anlage., S. M. Nonlinear time reversal in a wave chaotic system. Phys. Rev. Lett., 2013, 110, 063902.

  3. Dos Santos, S. and Plag, C. Excitation symmetry analysis method (ESAM) for calculation of higher order non-linearities. Int. J. Nonlinear. Mech., 2008, 43, 164–169.

  4. Ilison, L., Salupere, A., and Peterson, P. On the propagation of localized perturbations in media with microstructure. Proc. Estonian Acad. Sci. Phys. Math., 2007, 56, 84–92.

  5. Lomonosov, A. M., Kozhushko, V. V., and Hess, P. Laser-based nonlinear surface acoustic waves: from solitary to bondbreaking shock waves. In Proc. 18th ISNA. AIP, 2008, 1022, 481–490.

  6. Engelbrecht, J., Berezovski, A., Pastrone, F., and Braun, M. Waves in microstructured materials and dispersion. Philos. Mag., 2005, 85, 4127–4141.

  7. LeVeque, R. J. Finite-volume methods for non-linear elasticity in heterogenous media. Int. J. Numer. Meth. Fl., 2002, 40, 93–104.

  8. Berezovski, A., Berezovski, M., and Engelbrecht, J. Numerical simulation of nonlinear elastic wave propagation in piecewise homogeneous media. Mat. Sci. Eng., 2006, 418, 364–369.

  9. Haupert, S., Renaud, G., Rivière, J., Talmant, M., Johnson, P. A., and Laugier, P. High-accuracy acoustic detection of nonclassical component of material nonlinearity. J. Acoust. Soc. Am., 2011, 130, 2654–2661.

10. Vallikivi, M., Salupere, A., and Dai, H.-H. Numerical simulation of propagation of solitary deformation waves in a compressible hyperelastic rod. Math. Comput. Simulat., 2012, 82, 1348–1362.

11. Porubov, A. Amplification of Nonlinear Strain Waves in Solids. Series on Stability, Vibration, and Control of Systems. World Scientific, 2003.

12. Kliakhandler, I. L., Porubov, A. V., and Velarde, M. G. Localized finite-amplitude disturbances and selection of solitary waves. Phys. Rev. E, 2000, 62, 4959–4962.

13. Salupere, A., Lints, M., and Engelbrecht, J. On solitons in media modelled by the hierarchical KdV equation. Arch Appl. Mech., 2014, 84, 1583–1593.

14. Solodov, I. Y., Krohn, N., and Busse, G. CAN: an example of nonclassical acoustic nonlinearity in solids. Ultrasonics, 2002, 40, 621–625.

15. Gil, A., Segura, J., and Temme, N. Numerical Methods for Special Functions. Society for Industrial Mathematics, 2007.

16. Trefethen, L. N. Spectral Methods in MATLAB. SIAM, 2000.

17. Brown, P. N., Byrne, G. D., and Hindmarsh, A. C. VODE: A variable-coefficient ode solver. SIAM J. Sci. Stat. Comp., 1989, 10, 1038–1051.

18. Jones, E., Oliphant, T., Peterson, P. et al. SciPy: open source scientific tools for Python, 2001. (accessed 12.08.2014).

19. LeVeque, R. J. and Yong, D. H. Solitary waves in layered nonlinear media. SIAM J. Appl. Math., 2003, 63, 1539–1560.

20. Dos Santos, S., Vejvodova, S., and Prevorovsky, Z. Nonlinear signal processing for ultrasonic imaging of material complexity. Proc. Estonian Acad. Sci., 2010, 59, 108–117.

Back to Issue