Aeolian Liquid Vibrations in Conical Tanks with Baffles under Wind Loading with Fuzzy Parameters

Abstract

The Aeolian liquid vibrations in conical reservoirs caused by low-velocity, steady winds have been under consideration. Both amplitudes and dominant frequencies of wind loadings have been constantly changed, so to adequately describe the vibration process, fuzzy logic methods have been applied. At the first stage, the crisp initial value problem for conical shells with and without baffles has been considered. The liquid inside the reservoirs has been supposed to be an incompressible and ideal one, and its flow induced by the forced harmonic excitation, has been considered as potential. So, there exists a potential to satisfy the Laplace equation. The impermeable condition has been used at wetted surface boundaries of the shell, whereas the dynamic and kinematic boundary conditions have been set on the free liquid surface. A system of singular integral equations has been obtained for values of the velocity potential and the function describing the free surface rise. Its solution has been gained by boundary element methods. The crisp boundary value problem has been reduced to the second-order system of differential equations. After receiving the crisp solution of this system, the initial data have been fuzzified, involving triangular fuzzy numbers, and the fuzzy initial value problem has been formulated. The numerical solution to this problem with uncertain intervals involved has been obtained and analyzed.