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Information × Registration Number 0223U002908, 0119U103784 , R & D reports Title An approximate solutions construction for nonlinear problems of harmonic and single waves propagation in elastic materials popup.stage_title Head Rushchitskii Iarema Ya., Доктор фізико-математичних наук Registration Date 16-03-2023 Organization S.P.Timoshenko Institute of Mechanics popup.description2  Within the framework of the Murnaghan model, a nonlinear plane longitudinal elastic displacement wave for two forms of the initial profile - harmonic and bell-shaped - was studied theoretically and numerically. The main news is that the evolution of waves is analyzed by approximate methods taking into account the first three approximations. The analysis of the harmonic wave is considered only for comparison with the new results for the bell-shaped wave. Some significant differences between the wave evolution are shown. First, the initially symmetrical profiles are transformed as a result of evolution in a distorted manifold: the harmonic profile is symmetrical and the bell-shaped profile is asymmetrical. Second, the third approximation introduces a fourth harmonic for the harmonic wave when this wave was analyzed by the method of subsequent approximations, while the bell-shaped wave is characterized in the third approximation by another within the analysis by the displacement gradient constraint method. At some long distances from the beginning of wave propagation, a single-humped bell-shaped wave turns into a double-humped one. These humps are adjacent to each other and halve their soles. The third approximation makes it possible to observe new wave effects: the asymmetry of the left and right humps only of their peaks and the asymmetry of the humps relative to each other - the lowering of the left and right humps. The results of the study are commented. Product Description popup.authors Hamsheieva Olena A. Dashko Olha G. Romanova Natalia V. Savelieva Kateryna V. Khotenko Iryna M. Khotenko Olena O. Yurchuk Vasyl M. popup.nrat_date 2023-03-16 Close