Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Influence of the fluid free surface on the nonlinear resonance curves of a flexible tank partially filled with fluid
Submission Author:
Frederico Martins Alves da Silva , GO , Brazil
Co-Authors:
Ericka Hansen, Frederico Martins Alves da Silva
Presenter: Frederico Martins Alves da Silva
doi://10.26678/ABCM.COBEM2021.COB2021-0379
Abstract
A flexible partially fluid-filled tank is analyzed considering the tank as a simply supported cylindrical shell described by the Donnell’s nonlinear shallow-shell theory. The perturbation method is used to choose an appropriate displacement field to discretize the equilibrium equations. An external harmonic load is applied in the transversal direction with the shape of the first natural mode of vibration. The internal fluid, initially considered inviscid and irrotational, can be described by a potential flow and in a linear analysis, the velocity potential can be divided in two parts. The first one is responsible to describe the movement of the fluid body, that follows the velocity of the flexible tank and implies a velocity boundary condition that forces the fluid and the structure to have the same velocity in their interface. The second velocity potential contribution represents the free surface vibration, also known as sloshing. But in this situation, the tank is rigid, and this parcel must be added to the first one. By the Euler’s equilibrium equation, a hydrodynamic pressure is derived from the velocity potentials and applied in the tank walls. The same equation is used in the free surface with aim to guarantee the equilibrium in this region, called as sloshing equation, where a damping term is added using the Rayleigh dissipation function. With the coupled system composed by the tank nonlinear equilibrium equation with an applied hydrodynamic pressure and the sloshing equation, the Garlerkin method is used and, at last, the brute force method is employed to obtain the nonlinear resonance curves. Time responses, phase-portraits and Poincaré section are also obtained for different regions of the resonance curves, showing the nonlinear behavior of the coupled fluid-structure problem.
Keywords
cylindrical shell, Free surface, Nonlinear Dynamic, resonance
