Torsional elastic waves. Some aspects of nonlinear analysis

Authors

  • V. M. Yurchuk S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv
  • S. V. Sinchilo S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv https://orcid.org/0009-0004-3549-9187

DOI:

https://doi.org/10.17721/1812-5409.2023/2.31

Keywords:

boundary conditions, nonlinear torsional wave, five-constant Murnaghan potential, peculiarities of analysis of boundary conditions

Abstract

The features of the use of boundary conditions in the nonlinear problem of torsional wave propagation for an elastically deformable medium with an external boundary are analyzed. The formulation and wave analysis in the linear (classical) approach are briefly described, since the linear solution is used in the work as a first approximation in the nonlinear approach. The first feature for a torsional wave is a significant complication in the nonlinear approach of the boundary conditions due to the difference between the shape of the boundary before and after the deformation (in the linear approach, the shape of the boundary does not change). The second feature is the significant complication of the mathematical representation of the boundary conditions due to the appearance of additional nonlinear terms. For a torsional wave, it was found that the use of the condition of absence of stresses on the boundary surface (assumption of a free boundary) may not be completely correct.

Pages of the article in the issue: 172 - 175

Language of the article: Ukrainian

References

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Published

2023-12-23

How to Cite

Yurchuk, V. M., & Sinchilo, S. V. (2023). Torsional elastic waves. Some aspects of nonlinear analysis. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, (2), 172–175. https://doi.org/10.17721/1812-5409.2023/2.31

Issue

Section

Differential equations, mathematical physics and mechanics