VIBRATIONS OF STRUCTURE ELEMENTS UNDER PERIODIC LOADS WITH FLUID-STRUCTURE INTERACTION EFFECTS

Abstract

Much of modern power equipment operates in interaction with the environment. High fluid velocities cause significant pressure on the surface of structural elements. In turn, the oscillation of the elements of machines and structures in the fluid flow leads to a change in the parameters of fluid motion. That is, there is a related problem of determining the strength and dynamic characteristics of such systems. On the one hand, the oscillations of the elastic body change the parameters of the flow, and on the other hand, the presence of the flow leads to a significant impact on the dynamic characteristics of the structure. From the point of view of mechanics, such problems can be classified as problems of interaction of various continuous environments. To describe the motion of continuous media, use general equations of motion, equations of state, conservation laws. Different continuous media differ in the different relationship between the components of stress tensors and strain or strain rate tensors. Using the method of weighted residuals, the basic relations for determining the generalized displacements are obtained. The general formulation provides for the possibility of determining the frequencies and forms of natural oscillations of the structure without taking into account the attached masses of the liquid, taking them into account, as well as to investigate the forced oscillations of structural elements taking into account and without taking into account interacting with the liquid. For a viscous compressible fluid, the formulation of the problem in the acoustic approximation is obtained. Numerical realization is carried out under the assumption of vortex-free motion of an ideal and incompressible fluid. To solve the problem of determining the pressure of a liquid, we obtain the Laplace equation with non-flow conditions as boundary conditions. The problem of determining the hydrodynamic pressure using the methods of potential theory is reduced to solving a hypersingular integral equation. The forms of natural oscillations of the structural element without taking into account the attached masses of the liquid are chosen as the basic ones for solving the problem of determining the dynamic characteristics taking into account the liquid. As an example, the natural frequencies and forms of oscillations of a round plate are considered both without taking into account the influence of the liquid, and with its taking into account. The harmonic oscillations of this plate are also investigated.