Overhead water tank shapes with depth-independent sloshing frequencies for use as TLDs in buildings

Sloshing water in the overhead water tank of a multi-storeyed building may be utilized to act as a tuned liquid damper for vibration control under wind and earthquake excitation. In conventional rectangular or circular water tanks, tuning presents difficulties as the sloshing frequency varies significantly with change in the depth of water in the tank. To address this issue, in this paper, we find shapes of tanks wherein the sloshing frequency is essentially independent of water depth over a large and useful range of water levels. Both two-dimensional as well as axisymmetric (three-dimensional) tank shapes are found. We use a direct boundary element method to find the sloshing frequencies in each case. In each case, a tentative simple analytical form for the tank shape is chosen with three free parameters, and these parameters are adjusted to obtain shapes where the first lateral sloshing frequency has negligible variation with water depth. For axisymmetric tanks, the circumferential (azimuthal) variation in field variables is restricted to the first harmonic, in the interest of lower computational effort. For both planar and axisymmetric cases, the working range of water depths is taken to be from 0.2 to 2 times the tank width. In both cases, the variation in first lateral sloshing mode frequency is found to be under 0.2%over the working range. In comparison, for constant width tanks such as the rectangular or circular ones, over the same range of water depths, the corresponding variation is more than 60 times greater.