On Vibration of a Rectangular Tank filled with Water-VII

Abstract

When side walls of a ractangular tank, which is filled with water, are vibrating, the inside water will also make a vibratory motion. This motion of water lowers considerably the natural frequency of vibration, of side-walls of the tank. This effect is conveniently expressed by “virtual mass” of water. In the previous reports, I to VI, of the same title, the author has made a theoretical study on the value of the “virtual mass”, and examined various factors affecting it. These calculations were made by assuming, tentatively, the mode of vibration of rectangular elasticplate which constitute the side-walls of the tank. And, the velocity potential for the vibratory motion of water, caused by this vibration of sidewalls, was found. The question of degree of accuracy of the result obtained by this method, will naturally be raised, and some examination was made in report II of the same title.
In the present report, this question of degree of accuracy of the author's procedure in previous reports, is examined. It may be said that, we are dealing with a problem of hydro-elasticity. Here, the equation of vibratory motion of a rectangular elastic-plate subjected to lateral load (which is the water pressure caused by vibratory motion of water), is taken as the basis of our discussion. And magnitudes of correction terms are deduced from it. It is concluded that, at least for rectangular plates of ordinary proportions, the approximate formula given in previous reports, may be said to be fairly accurate.