Liquid oscillation in a rectangular tank with a core barrel (Condition for internal resonance)

Abstract

The nonlinear liquid motion in a partially filled rectangular tank with a core barrel is investigated. Basic equations are derived by employing the variational principle. Unlike in case of a rectangular tank without a core barrel, it is difficult to obtain analytically the modes of vibration and the natural frequencies of the liquid motion in a rectangular tank with a core barrel. Therefore, the modes of vibration and the natural frequencies are obtained by using the finite elements method. It was shown by the previous research on the nonlinear liquid motion in a rectangular tank that the internal resonance may occur at the water depth where the natural frequency of the second mode accords with twice the natural frequency of the first mode. In case of a rectangular tank with a core barrel, the water depth satisfying this condition was found by the relations between water depth and the natural frequency. An experiment was carried out at this water depth using the model tank. The occurrence of the internal resonance was confirmed by the experimental results. The effects of radius and location of a core barrel on the condition of the internal resonance was discussed. It is shown that the water depth where the internal resonance occurs becomes higher as the radius of a core barrel becomes larger or that location becomes closer to the center of the tank.

Keywords

• nonlinear vibration
• liquid sloshing
• rectangular tank with a core barrel
• internal resonance
• horizontal excitation