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Applied mathematics
Analysis of the phase structure of fluid vibrations with floating longitudinally compressed elastic plate in nonlinear interaction of the surface progressive waves
A. A. Bukatov Marine Hydrophysical Institute of the Russian Academy of Sciences, 2, Каpitanskaya ul., Sevastopol,
299011, Russian Federation
Abstract:
Based on the asymptotic expansions obtained by the multi-scale method up to the third order
of smallness for the potential velocity of liquid particles and the plate-fluid surface elevation,
the dispersion properties of the vibrations generated by the interaction of progressive surface
wave harmonics of finite amplitude are analyzed in the article. The effect of nonlinearity of
acceleration of vertical displacements of an elastic plate on the dispersion characteristics of
wave disturbances is studied. The dependence of the vibration frequency is estimated by
taking into account the nonlinearity of the first and second approximations values, the plate
thickness, and the longitudinal compressive force. It is shown that the sign of the amplitude
of the second interacting harmonic and the nonlinearity of the acceleration of vertical
displacements of the longitudinally compressed elastic plate affect the vibration phase. It
was found that with a decrease in the wavelength of the initial harmonic, the influence of the
plate’s nonlinearity vertical acceleration is enhanced. The presence of compressive force is
manifested in a decrease in the frequency of vibrations of the wave disturbance in comparison
with the frequency obtained in the absence of longitudinal compression, both with a positive
and negative sign of the second interacting harmonic amplitude.
Keywords:
ice plate fluctuations, waves of finite amplitude, nonlinear interaction of waves,
flexural deformation of a plate, longitudinal compressive force, phase characteristics.
Received: January 20, 2020 Accepted: August 13, 2020
Citation:
A. A. Bukatov, “Analysis of the phase structure of fluid vibrations with floating longitudinally compressed elastic plate in nonlinear interaction of the surface progressive waves”, Vestnik S.-Petersburg Univ. Ser. 10. Prikl. Mat. Inform. Prots. Upr., 16:3 (2020), 226–237
Linking options:
https://www.mathnet.ru/eng/vspui453 https://www.mathnet.ru/eng/vspui/v16/i3/p226
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Abstract page: | 77 | Full-text PDF : | 16 | References: | 19 | First page: | 3 |
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