Vibration analysis of cylindrical liquid storage tanks that considers excitation phase difference

Abstract

An investigation is described of the hydroelastically coupled motion of a cylindrical tank partially filled with liquid in response to travelling seismic wave excitation. The continuous phase variation of the vertical excitation along the base causes flexible tank wall vibration modes with positive circumferential wave numbers. The stress analysis for this crucial case is conducted in this paper. An analytical explanation of the wave velocity dependences of the circumferential wave components of the stress cannot readily be given because the sinusoidal excitation term has a trigonometric function in its argument. To enable such an explanation, the travelling seismic wave is expressed in terms of the Bessel function. A stochastic response analysis is also conducted. Solving moment equations becomes difficult because the determination of their excitation terms requires a quadruple integral over the Duhamel time-integral interval for each present time. To solve this problem, the exponential term in the auto-correlation function of the excitation is expressed by a Fourier series.

Keywords

• vibration of continuous system
• fluid induced vibration
• vibration coupled with fluid motion
• excitation phase difference
• stochastic response analysis