Free vibration analysis of coupled sloshing-flexible membrane system in a liquid container

Abstract

A finite element model is developed to study free vibration of a liquid in a tank of arbitrary geometry with a flexible membrane constraining the liquid free-surface. A variational formulation is initially developed using the Galerkin method, assuming inviscid, incompressible and irrotational flow. The resulting generalized eigenvalue problem is then reduced by considering only the elements on the liquid free-surface, which significantly reduces the computational time. The proposed physical model is subsequently implemented into the FEniCS framework to obtain coupled hydroelastic liquid-membrane frequencies and modes. The coupled frequencies are compared with those reported for rectangular and upright cylindrical tanks using analytical methods in order to illustrate the validity of the finite element model. The results are subsequently presented for a horizontal cylindrical tank with an elastic free-surface membrane for different fill ratios and tank lengths. The effects of the membrane tension on the free vibration of the liquid in the tank are further investigated by comparing the coupled liquid-membrane frequencies with slosh frequencies of the liquid alone. It is shown that sloshing frequencies can be effectively shifted to higher values to prevent resonance in partially filled moving containers.

Study of Faraday waves in tanks in presence of polystyrene bead layers

“…4). These beads can also be considered as an elastic membrane [18]. This membrane applies a pressure on the liquid's surface, restraining its movement.…”

Liquid vibrations in a container with a membrane at the free surface

“…The solutions of this problem are own modes and own frequencies, 𝜔 , 𝑤 = 𝑤 (𝑟)cos𝑚𝜃. These modes and frequencies are reported in [14]. To obtain the solution of coupled problem the next series is used for each 𝑚:…”

“…The vibrations of liquid in cylindrical tanks with and without baffles on the free surface under horizontal and vertical excitation are reported in [13]. The problem of sloshing in horizontal elliptical tanks with T-shaped baffles is investigated in [14]. Many researchers have been investigating the membrane's dynamic response due to sloshing.…”