Fuzzy Analysis of Fluid Vibrations in Liquid Storage Tanks under Wind Loads

The paper is devoted to Aeolian liquid vibrations in reservoirs caused by low-velocity, steady winds. Amplitudes and dominant frequencies of the wind load are constantly changing, so fuzzy logic methods are the most suitable mathematical apparatus for describing the problem. It is supposed that the load amplitudes and frequencies are characterized by fuzzy numbers. At first stage the solution of the crisp initial value problem is obtained. A cylindrical rigid thin-walled shell is used as the tank model. The considered ideal fluid is assumed to be incompressible, and its motion is potential. These suppositions make it possible to provide the potential of velocities, which, as a result of the above assumptions, satisfies the Laplace equation. At the rigid boundaries of the liquid volume, the conditions of non-flow are satisfied, and the free surface is subjected to kinematic and dynamic boundary conditions. First, a crisp boundary value problem is solved, which is reduced to a system of differential equations, then the initial data and loading parameters are fuzzified using triangular fuzzy numbers. Finally, the analysis of the numerical solution of the fuzzy boundary value problem is carried out.