Abstract
Vibrations of an ideal incompressible fluid in shells of revolution have been considered. The shells of revolution under consideration include cylindrical and conical parts. It is assumed that the shell is subjected to vertical and horizontal excitations. The liquid in the shells is supposed to be an ideal and incompressible one. The fluid flow is the irrotational. Therefore the velocity potential that satisfies the Laplace equation exists. The non-penetration conditions are applied to the wetted surfaces of the shell and the kinematic and dynamic conditions on the free surface have been considered. The liquid pressure as the function of the velocity potential is defined using the Bernoulli equation. The problem of determining the fluid pressure is reduced to solving a singular integral equation. The numerical solution of the equation has been obtained by the method of discrete singularities. The method of simulating the free and forced oscillations of the fluid in the shells of revolution has been developed.
Highlights
Shell structures for storage and transportation of fluid are the subject of numerous scientific researches
These shell structures are important for power plants, pumps, columns of oil evaporators, and other industrial constructions
There are a large number of various strength and vibration problems for shell structures that have been examined in recent decades
Summary
Shell structures for storage and transportation of fluid are the subject of numerous scientific researches. The problem of oscillation of a fluid in a compound rotation shell having cylindrical and conical parts has been considered. Shell rotation with fluid and the forms of oscillations of free surface. For solving the forced oscillation problem we consider the Bernoulli equation (2.1) on a free surface. We represent the velocity potential in form (3.1), and write the function describing the position of the free surface as follows: ζ=. The functions φk are modes of free fluid oscillation in a rigid tank They are obtained by solving boundary-value problem (2.2). It should be noted that according to [7, 10], the frequencies and modes of oscillations of the fluid are considered to correspond to certain harmonics, it is assumed that the velocity potential and the function describing the level of lifting of the free surface.
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Schedule a callMore From: Bulletin of V.N. Karazin Kharkiv National University, series «Mathematical modeling. Information technology. Automated control systems»
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