Study on Vibration of a Floating Roof of an Oil Storage Tank Due to Nonlinear Sloshing

Vibration of a floating roof due to nonlinear sloshing is investigated theoretically in this paper. First, a variational principle is introduced based on the equality between the liquid pressure and the Lagrangian density of the liquid. The floating roof is modeled by a finite element approach. A weighted-residual form of the governing equations is transformed into time-domain nonlinear ordinary differential equations to be solved by the Galerkin method. Numerical results show that stress responses obtained by the nonlinear analysis are larger than those obtained by the linear analysis. This is due to the fact that internal resonance occurs because the natural frequency of a mode with circumferential wave number 2 is twice the natural frequency of the radial first mode with circumferential wave number 1. Examination of the mode shapes of the floating roof shows that although the vibration amplitude is large over the deck and is small at the pontoon in most of the modes, a mode with significantly large vibration amplitude at the pontoon exists for the circumferential wave number 2. When this type of mode undergoes the internal resonance, stresses become very large in magnitude and exceed the levels that are predicted by the linear analysis.