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. In work different ways of fixing of a beam on the ends were considered: hinged and rigid. Thecase of rigid restrictions imposed on the thickness of the plate was also investigated. For all considered methodsof fixing numerical calculations which results are presented on the corresponding schedules were carried out. The paper investigates the problem of optimizing the frequencies of an elastic plate oscillating in an idealfluid. The formulation of the corresponding problem of hydroelasticity is given. By methods of the theory offunctions of complex variable the solution of an external hydrodynamic problem is received and the forcesacting from liquid on oscillating plate are defined. With the help of ideas and methods proposed in [1, 5],an integro-differential equation describing one-dimensional oscillations of a plate in a liquid is obtained. Aformal mathematical formulation and study of the optimization problem are given. The numerical algorithm fordetermining the optimal forms and the results of calculations on the PC.