Fundamental modes of tank-liquid systems under horizontal motions

This paper reports results on the fundamental impulsive modes of vibration of cylindrical tank-liquid systems anchored to the foundation under horizontal motion. The analyses are performed using a general purpose finite element (FE) program, and the influence of the hydrostatic pressure and the self-weight on the natural periods and modes is considered. The roof and walls are represented with shell elements and the liquid is modeled using two techniques: the added mass formulation and acoustic finite elements. Tank height to diameter ratios from 0.40 to 0.95 were used, with a liquid level at 90% of the height of the cylinder. The effect of the geometry on the fundamental modes for the tank-liquid systems is studied using eigenvalue and harmonic response analyses. Similar fundamental periods and mode shapes were found from these two approaches. The fundamental modes of tank models with aspect ratios (H/D)(H/D) larger than 0.63 were very similar to the first mode of a cantilever beam. For the shortest tank (H/D=0.40)(H/D=0.40), the fundamental mode was a bending mode with a circumferential wave n=1n=1 and an axial half-wave (m)(m) characterized by a bulge formed near the mid-height of the cylinder.