Study of Correlation Between Beam Vibration and Oval Vibration on Cylindrical Water Storage Tank

Abstract

A large cylindrical water storage tank, widely used at power stations and chemical plants, typically has a large radius/wall-thickness ratio. The relatively thin sidewall of such a tank can deform easily during an earthquake due to vibrations of the tank structure. In order to improve the seismic-proof design practices for a water storage tank of flexible structure and to develop a new seismic resistance evaluation method to be adopted in future, it is important to understand the dynamic responses of such a tank to seismic motions including the nonlinearity of responses to large amplitude vibrations. This paper reports on the results of vibration test, in which sinusoidal wave excitations with large amplitude were conduced to the scale model tank of a thin-walled cylindrical water storage tank, and the theoretical analysis of the dynamics of the vibratory behaviors that were observed during the vibration test. First, a frequency sweep test was performed over the range that covered the natural frequency. The response of the test tank as a whole to given vibrations remained almost the same over the excitation frequency range. Frequency analysis of the response of the tank failed to locate any resonance points at or around frequencies that had been determined by the basic vibration characteristic test that we had conducted in advance. Next, a large amplitude excitation tests were carried out, in which the test tank was excited intensively by several tens of sinusoidal waves of a fixed frequency that was in the vicinity of the resonant frequency. The response of the tank as a whole in the form of beam vibrations did not intensify in proportion to the input acceleration; it did not go beyond a certain level. Since both of the tests produced significant oval vibrations on the sidewall of tank, the influence of oval vibrations over beam vibrations was analyzed. The analysis concerning the deflection of the sidewall of tank by the additional appearance of oval vibrations in the presence of beam vibrations revealed that a major decrease in the flexural rigidity reduced the response (beam vibrations) of the whole tank. The phenomenon was modeled using a nonlinear equation of motion, assumed that the rigidity depended on the amplitude of oval vibrations. The analysis using this equation explained the results of the above-mentioned tests very well. Thus, it was demonstrated both empirically and analytically that beam vibrations of a cylindrical water storage tank are reduced by the appearance of oval vibrations that have the effect of lowering the natural frequency.