Liquid oscillation in a cylindrical-conical shell under the action of vertical and horizontal excitation

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.