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Registration Number

0224U002557, 0119U103784 , R & D reports

Title

An approximate solutions construction for nonlinear problems of harmonic and single waves propagation in elastic materials

Head

Rushchitskii Iarema Ya., Доктор фізико-математичних наук

Registration Date

19-02-2024

Organization

S.P.Timoshenko Institute of Mechanics

Description

Within the framework of Mernagan's five-constant model of the nonlinear theory of elasticity, a nonlinear elastic plane longitudinal displacement wave was studied theoretically and numerically for three forms of the initial profile - harmonic periodic symmetric, Gaussian (single symmetric single hump), Whittaker (single nonsymmetric single hump). The main novelty is that the evolution of waves is analyzed by approximate methods, taking into account the first three approximations. The harmonic wave analysis is considered only for comparison with the new results for single waves. Some significant differences between the evolution of waves are shown. The results of the study are commented and a comparison of the evolution scenarios selected for the analysis of the three waves is carried out. Some practical recommendations are formulated that can be useful in the development of simple engineering models of the action of single waves on structures and their elements.

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Hamsheieva Olena A.
Dashko Olha H.
Romanova Nataliia V.
Savelieva Kateryna V.
Khotenko Iryna M.
Khotenko Olena O.
Yurchuk Vasyl M.