Analytical evaluation of dynamic characteristics of unanchored circular ground-based steel tanks

Natural and rocking frequencies of liquid-filled unanchored cylindrical steel tanks are determined using an analytical approach. In the proposed simplified mechanical model, the bottom plate of the tank is replaced by equivalent rotational and vertical springs. To evaluate natural frequencies, potential and kinetic energies of the liquid-filled tank are utilized and the eigen equation is solved by applying the Lagrange method and Ritz-type mode shapes for elastically supported cylindrical shells. Formulas are also derived to determine the rocking frequency based on a rotational rigid body motion and results are verified with available experimental data. Also, effect of the increase in kinetic energy of the tank during rocking motion on the natural frequencies of the tank is explored. To investigate the effects of tank geometrical aspect ratios on the structural responses, three models with height to diameter ratios of 0.4 (squat tank), 0.63 (medium tank) and 0.9 (slender tank) are considered. The results obtained using the proposed simplified mechanical model indicate that the method is capable of determining the rocking frequency of unanchored steel liquid-filled tanks with acceptable accuracy. Also, it is shown that at the onset of rocking mode, the fundamental natural frequency of the tank decreases considerably.