by I. P. Gavriljuk, M. Hermann, I. Lukovsky, O. Solodun, A. Timokha
Preprint series: 06-26, Reports on Numerical Mathematics
I. P. Gavriljuk, M. Hermann, I. Lukovsky, O. Solodun, A. Timokha
Preprint series: , Reports on Numerical Mathematics
Abstract: Conical-shaped or conical-bottom reservoirs are widely used as water containment for elevated tanks.
After earthquakes water tanks play an important role, by making the water available needed for
extinguishing fires which arise with such catastrophic events frequently. Therefore special care must
be practiced with the construction of the tanks in order to assure their safety and functionality during
a seismic event. The occurrence of resonant vibrations caused by the closeness of the lowest natural
sloshing frequency of the contained water to the effective frequency domain of seismic excitations is
very dangerously. Robust and CPU-efficient numerical methods are therefore required for quantifying
the natural sloshing frequencies and modes. The present paper employs the Treftz variational scheme
and two distinct harmonic basic systems of functions to develop two numerical-analytical methods.
Extensive numerical experiments establish the limits of their applicability in terms of semi-apex angle
and position of the truncating plane.
Keywords: Linear sloshing frequencies, the Treftz method