Lateral Free Vibration of Liquid-Storage Tanks

Abstract

Liquid filled tanks play an important role in the infrastructure of many industrial facilities assuring the supply with raw material needed for the production process or serving as storage for intermediate products. Due to their oftentimes large dimensions in diameter and height the stored fluid develops high seismic loads to the tank shell induced by the vibration of the liquid and the interaction of shell and liquid. In the design of tank shells the determination of the seismically induced pressure to the tank shell and the resulting overturning moments pose some challenges in engineering practice, especially with respect to the impulsive load component (interaction of shell and liquid). The following paper presents two different methods to calculate the eigenperiod, the eigenmode and the associated hydrodynamic pressure distribution for thin cylindrical liquid storage tanks for the circumferential wave number m=1 (lateral ground excitation). The first method includes an improved variation of the added-mass-iteration scheme: It employs a Rayleigh quotient’s formulation of the liquid-shell free vibration and repetitively manipulates the distribution of the kinetic energy of the fluid until convergence occurs. The second method involves the calculation of the added mass matrix directly from the appropriate expression for the work done by the liquid-shell interface forces on the basis of the radial displacement shape functions. The closed form solution of the governing matrix equation of motion of the shell enables the computation of higher eigenmodes and no iterative procedure is required.