A computational investigation of vibration of stationary and rotating structures submerged in a liquid

Abstract

To realize some technological processes components of a number of stationary and rotating machines work submerged in various liquids. Therefore their vibration is significantly influenced by their interaction with the medium in the surrounding space. An important tool for investigation of their behavior is a computer modelling method. In the computational models it is assumed that the vessel and the submerged bodies are absolutely rigid, the liquid is perfect and incompressible, amplitude of the vibration is small, and the flow and the oscillations are 2D. On these assumptions the pressure distribution in the liquid is described by a Laplace equation. For its solution a finite element or a finite difference methods can be used. The region filled with the liquid is, in general, of irregular shape. To describe its geometry or to perform its discretization the B´ezier surfaces can be utilized. In the cases when the region filled with the liquid changes its boundaries there is a possibility to transform solution of the governing equation from the primary region into the unit square domain making use of the dimensionless coordinates. The advantage is that this approach does not require to change the discretization even if the primary region changes its shape. On the other hand the form of the transformed equation is more complicated than the form of the original one.