Analysis of the phase structure of fluid vibrations with floating longitudinally compressed elastic plate in nonlinear interaction of the surface progressive waves

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.