Effect of Pre-stress States on the Impulsive Modes of Vibration of Cylindrical Tank-liquid Systems under Horizontal Motions

Abstract

In this paper we investigate the influence of hydrostatic pressure and self-weight loads (pre-stress state) on the natural periods and mode shapes of steel cylindrical tanks and on the response under horizontal motions. The tank structure is modeled with finite elements and added mass models are used to represent the liquid. Only the impulsive component of the hydrodynamic response is considered. The natural periods and mode shapes for tank-liquid systems including and neglecting the effect of the pre-stress state are computed and compared. Three tank-liquid systems with different cylinder height to diameter ratios and slenderness ratios are considered. The numerical results show that the pre-stress state has a significant influence in the natural periods and mode shapes of tank-liquid systems with thinner walls; however, for thicker shells this effect is reduced. When the pre-stress state is neglected and included, the smaller differences in natural periods occur, for modes characterized by small circumferential wavenumbers. The steady-state response of a tank-liquid system to horizontal harmonic base accelerations was also computed. Large differences were found when the pre-stress state was neglected. A comparison of the frequency response functions shows that the peak responses occur at quite different load periods and they have significantly different amplitudes.