Optimization of vibration frequencies of the elastic plate in anideal fluid

In this paper, we consider the problem of optimizing the vibration frequency of the elastic plate, which iscompletely immersed in the ideal liquid. The model of small oscillations of a plate in this case is an integro-differential equation with the appropriate boundary conditions. This problem is considered as a model examplein the book Banichuk N. B. [5]. The peculiarity of this problem is a special kind of functional equation, whichsatisfies the function of deflection of the plate from the equilibrium position. Due to the fact that the integraloperator is self-adjoint, it was possible to obtain the necessary extremum conditions, on the basis of which anoriginal numerical algorithm for optimizing the oscillation frequencies was developed. The search for the solutionof the optimization problem is based on the method of gradient design, this work has been obtained exactformulas for finding the projection of the gradient. Using the method of hydrodynamic potentials the problem of plate oscillation was reduced to the problemof beam oscillation...