Atypical evolution of solitary wave propagating in nonlinear elastic medium

TitleAtypical evolution of solitary wave propagating in nonlinear elastic medium
Publication TypeJournal Article
Year of Publication2020
AuthorsRushchitsky, JJ, Yurchuk, VM
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2020.12.028
Issue12
SectionMechanics
Pagination28-37
Date Published12/2020
LanguageUkrainian
Abstract

The atypical evolution of a solitary cylindrical wave that propagates in the nonlinear elastic medium and has the initial profile in the form of the Macdonald function is described and commented. In the analysis, the approximate method of restriction on the gradient of a deformation is used, and three first approximations are taken into account. Two examples of typical wave evolution — harmoniс and bell-shaped waves — are shown and commented, where the first three approximations are also taken into account. The numerical modeling showed that the atypical initial profile (profile without a hump) evolves atypically — the profile becomes essentially steeper, saving the concavity, and the wave bottom decreases almost two times.

Keywordsevolution of a wave initial profile, Macdonald functions, method of res triction on the gradient of a deformation, solitary nonlinear elastic wave, three first approximations
References: 

1. Murnaghan, F. (1985). Finite Deformation in an Elastic Solid. Gloucester, MA, Peter Smith Publisher Inc., 3th ed., pp. 140.
2. Rushchitsky, J. J. (2014). Nonlinear Elastic Waves in Materials. Series: Foundations of Engineering Mechanics. Heidelberg: Springer.
3. Rushchitsky, J. J. (2012). Theory of Waves in Materials. Copenhagen: Ventus Publishing ApS.
4. Rushchitsky, J. J. (2019). Plane Nonlinear Elastic Waves: Approximate Approaches to Analysis of Evolution, Chap. 3 in the book “Understanding Plane Waves”. Ed. William A.Cooper. London: Nova Science Publishers.
5. Yurchuk, V. N. & Rushchitsky, J. J. (2017). Numerical Analysis of Evolution of the Plane Longitudinal Nonlinear Elastic Waves with Different Initial Profiles. Int. App. Mech., 53, No. 1, pp. 104-110. doi: 10.1007/s10778-017-0794-6