Hydroelastic vibrations of shells of revolution under combined vertical and horizontal loadings

Abstract

The operation of modern structures occurs under conditions of high technological loads. Shells of rotation are among the most applicable structural elements. The operating conditions of such elements provide for the influence of the environment such as the interaction of elastic shell elements with liquid or gas. The oscillations of the elastic shell of rotation, which are partially filled with liquid, under external loads in the vertical and horizontal directions simultaneously, are considered in the paper. The liquid is supposed to be ideal and incompressible, and its motion under the applied loads is irrotational. This allows us to introduce the velocity potential to calculate the pressure of the fluid on the surface of the shell and determine the function which describes the level of the free surface lift. At the first stage, the frequencies and forms of free oscillations of the shell with liquid are determined. These frequencies are usually divided into two separate spectra: the free surface vibration frequency and the elastic wall vibration frequency. The boundary element method is used for numerical implementation. It is found that for sufficiently thin elastic tank walls, the fundamental frequency of the coupled vibrations can be much lower than the frequency of the fluid in a shell with rigid walls. As the tank wall thickness increases, this effect becomes insignificant, and the lower vibration frequency of the shell with liquid approaches the vibration frequency of the liquid in a rigid tank. The second stage of the study is related to the analysis of combined horizontal and vertical loads. The cases when the load frequencies are close to the fundamental frequency of sloshing and to the lower frequency of vibration of elastic walls are considered. The effect of parametric resonance has been investigated. The influence of the presence of partitions on the motion of the shell with the liquid at free and forced oscillations has been found out.