Natural sloshing frequencies in rigid truncated conical tanks
Purpose - The main purpose of this paper is to develop two efficient and accurate numerical analytical methods for engineering computation of natural sloshing frequencies and modes i the case of truncated circular conical tanks. Design/methodology/approach - The numerical-analytical methods are based on a Ritz Treftz variational scheme with two distinct analytical harmonic functional bases. Findings - Comparative numerical analysis detects the limit of applicability of variational methods in terms of the semi-apex angle and the ratio between radii of the mean free surface and the circular bottom. The limits are caused by different analytical properties of the employed functional bases. However, parallel use of two or more bases makes it possible to give an accurate approximation of the lower natural frequencies for relevant tanks. For V-shaped tanks, dependencies of the lowest natural frequency versus the semi-apex angle and the liquid depth are described. Practical implications - The methods provide the natural sloshing frequencies for V-shaped tanks that are valuable for designing elevated containers in seismic areas. Approximate natural modes can be used in derivations of nonlinear modal systems, which describe a resonant coupling with structural vibrations. Originality/value - Although variational methods have been widely used for computing the natural sloshing frequencies, this paper presents their application for truncated conical tanks for the first time. An original point is the use of two distinct functional bases.
frequencies numerical analysis liquid flow containers