Skip to main content
SpringerLink
Log in

Distortion of a Nonlinear Elastic Solitary Plane Wave with Friedlander Profile*

  • Published:
International Applied Mechanics Aims and scope

The distortion of a nonlinear elastic plane displacement wave of Friedlander profile typical for blast waves is analyzed theoretically and numerically using the five-constant Murnaghan model. Contrary to most nonlinear waves in materials that have periodic or single humps, this wave has no hump, is monotonically decreasing, and is concave down. The evolution of waves is studied using an approximate method with the first two approximations taken into account. Some essential distinctions of this wave are shown in detail theoretically and numerically: its atypical profile evolves in an atypical way. The following significant features of the Friedlander wave are shown: the profile becomes much (for materials with soft nonlinearity) or less (for materials with hard nonlinearity) steeper, still has no hump, and remains convex down, the maximum value of the profile increasing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. N. Guz, Elastic Waves in Prestressed Bodies [in Russian], in two vols., Naukova Dumka, Kyiv (1986).

    Google Scholar 

  2. L. K. Zarembo and V. A. Krasil’nikov, Introduction to Nonlinear Acoustics [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  3. A. I. Lurie, Nonlinear Theory of Elasticity, North-Holland, Amsterdam (1990).

    MATH  Google Scholar 

  4. J. J. Rushchitsky, “On approximate analysis of the evolution of a compression wave propagating in an elastic medium,” Dop. NAN Ukrainy, No. 8, 46–58 (2019).

  5. J. J. Rushchitsky, “Atypical evolution of a solitary wave propagating in a nonlinear elastic medium,” Dop. NAN Ukrainy, No. 12, 34–58 (2020).

  6. J. J. Rushchitsky and S. I. Tsurpal, Waves in Microstructural Materials [in Ukrainian], Inst. Mekh. S. P. Timoshenka, Kyiv (1998).

    Google Scholar 

  7. M. Alonso and N. Reguera, “Numerical detection and generation of solitary waves for a nonlinear wave equation,” Wave Motion, 56, 137–146 (2015).

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Beli, J. R. F. Arruda, and M. Ruzzene, “Wave propagation in elastic metamaterial beams and plates with interconnected resonators,” Int. J. Solids Struct., 139–140, 105–120 (2018).

  9. C. Cattani and J. Rushchitsky, Wavelet and Wave Analysis as applied to Materials with Micro and Nanostructure, World Scientific, Singapore–London (2007).

    Book  MATH  Google Scholar 

  10. N. Chandra, S. Ganpule, N. N. Kleinschmit, R. Feng, A. D. Holmberg, A. Sundaramurthy, V. Selvan, and A. Alai, “Evolution of blast wave profiles in simulated air blasts: experiment and computational modeling,” Shock Waves, 22, 403–415 (2012).

    Article  Google Scholar 

  11. F. G. Freidlander, “The diffraction of sound pulses. I. Diffraction by a semi-infinite plate,” Proc. Roy. Soc. Lond., A, 186, 322–344 (1946).

    Article  Google Scholar 

  12. I. A. Guz and Y. Y. Rushchitskii, “Comparison of mechanical properties and effects in micro-and nanocomposites with carbon fillers (carbon microfibers, graphite microwhiskers, and carbon nanotubes),” Mech. Comp. Mater., 40, No. 3, 179–190 (2004).

    Article  Google Scholar 

  13. I. A. Guz, J. Rushchitsky, and A. N. Guz, “Modelling properties of micro- and nanocomposites with brush like reinforcement,” Math.-Wiss. und Werkstofftech., 40, No. 3, 33–39 (2009).

    Google Scholar 

  14. A. N. Guz and J. Rushchitsky, Short Introduction to Mechanics of Nanocomposites, Scientific and Academic Publishing, Rosemead (CA) (2013).

    Google Scholar 

  15. Y. Ishii, S. Biwa, and T. Adachi, “Second-harmonic generation of two-dimensional elastic wave propagation in an infinite layered structure with nonlinear spring-type interfaces,” Wave Motion, 97, No. 9, 102–569(2020).

    MathSciNet  MATH  Google Scholar 

  16. M. Kuriakose, M. Skotak, A. Misistia, S. Kahali, A. Sundaramurthy, and N. Chandra, “Tailoring the blast exposure conditions in the shock tube for generating pure, primary shock waves: The end plate facilitates elimination of secondary loading of the specimen,” PLoS ONE, 11, No. 9, e0161597 (2016).

    Article  Google Scholar 

  17. Z. N. Li, Y. Z. Wang, and Y. S. Wang, “Three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial,” Int. J. Non-Linear Mech., 125, No. 10, 193–531 (2020).

    Google Scholar 

  18. F. Murnaghan, Finite Deformation in an Elastic Solid, 3rd ed., Peter Smith Publisher, Gloucester, MA, USA (1985).

    Google Scholar 

  19. J. J. Rushchitsky, Theory of Waves in Materials, Ventus Publishing ApS, Copenhagen (2011).

    Google Scholar 

  20. J. J. Rushchitsky, “Certain class of nonlinear hyperelastic waves: classical and novel models, wave equations, wave effects,” Int. J. Appl. Math. Mech., 8, No. 6, 400–443 (2012).

    Google Scholar 

  21. J. J. Rushchitsky, Nonlinear Elastic Waves in Materials, Springer, Heidelberg (2014).

    Book  MATH  Google Scholar 

  22. J. J. Rushchitsky, “On constraints for displacement gradients in elastic materials,” Int. Appl. Mech., 51, No. 2, 119–133 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  23. J. J. Rushchitsky, “Plane Nonlinear Elastic Waves: Approximate Approaches to Analysis of Evolution,” Chapter in the Book W. A. Cooper (ed.), Understanding Plane Waves, Nova Science Publ., London (2019), pp. 201–220.

  24. J. J. Rushchitsky, Foundations of Mechanics of Materials, Ventus Publishing ApS, Copenhagen (2021).

    Google Scholar 

  25. J. J. Rushchitsky, “Scenarios of evolution of some types of simple waves in nonlinear elastic materials,” Arch. Appl. Mech., 91, No. 7, 3151–3170 (2021).

    Article  Google Scholar 

  26. J. J. Rushchitsky, C. Cattani, and S. V. Sinchilo, “Physical constants for one type of nonlinearly elastic fibrous microand nanocomposites with hard and soft nonlinearities,” Int. Appl. Mech., 41, No. 12, 1368–1377 (2005).

    Article  Google Scholar 

  27. J. J. Rushchitsky and V. M. Yurchuk, “One approximate method for analyzing solitary waves in nonlinearly elastic materials,” Int. Appl. Mech., 52, No. 3, 282–290 (2016).

    Article  MATH  Google Scholar 

  28. J. J. Rushchitsky and V. M. Yurchuk, “Numerical analysis of the evolution of plane longitudinal nonlinear elastic waves with different initial profiles,” Int. Appl. Mech., 53, No. 1, 104–110 (2017).

    Article  MathSciNet  Google Scholar 

  29. J. J. Rushchitsky and V. M. Yurchuk, “Effect of the third approximation in the analysis of the evolution of a nonlinear elastic P-wave. Part 1,” Int. Appl. Mech., 56, No. 5, 581–589 (2020).

    Article  MathSciNet  Google Scholar 

  30. J. J. Rushchitsky and V. M. Yurchuk, “Effect of the third approximation in the analysis of the evolution of a nonlinear elastic P-wave. Part 2,” Int. Appl. Mech., 56, No. 6, 666–673 (2020).

    Article  MathSciNet  Google Scholar 

  31. V. Hauk (ed.), Structural and Residual Stress Analysis, Elsevier Science B. V., Amsterdam (1997); e-variant (2006).

  32. V. N. Yurchuk and J. J. Rushchitsky, “Numerical analysis of evolution of plane longitudinal nonlinear elastic waves with different initial profiles,” Int. App. Mech., 53, No. 1, 104–110 (2017).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St, Kyiv, 03057, Ukraine

    J. J. Rushchitsky & V. M. Yurchuk

  2. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, 37 Peremogy Av, Kyiv, 03056, Ukraine

    J. J. Rushchitsky & V. M. Yurchuk

Authors
  1. J. J. Rushchitsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. M. Yurchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. J. Rushchitsky.

Additional information

*This study was sponsored by the budgetary program Support of Priority Areas of Research (KPKVK 6541230).

Translated from Prykladna Mekhanika, Vol. 58, No. 4, pp. 21–31, July–Augus 2022.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rushchitsky, J.J., Yurchuk, V.M. Distortion of a Nonlinear Elastic Solitary Plane Wave with Friedlander Profile*. Int Appl Mech 58, 389–397 (2022). https://doi.org/10.1007/s10778-022-01164-z

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-022-01164-z

Keywords

Search

Navigation