矩形水槽壁の接水振動について (第6報)

抄録

When side-walls of a rectangular 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 V, of the same title, the author has made theoretical studies on the value of “virtual mass” of water, and examined various factors affecting it. The present report, which is the continuation of the same study, the case is examined wherein two opposite (rectangular) side-walls are vibrating in a mode which correspond to the case of “rectangular plate with clamped edges”. Approximate formula for the fundamental frequency of free vibration of the system (consisting of rectangular elastic plates and water), is given. The result is shown as graphs, which give values of coefficient M of virtual mass of water, for different values of B/L and B/H. (B=breadth, H=height, L=length of the rectangular water tank.)
In addition, a case is examined, wherein the upper edge-lines of the tank is vibrating, instead of being kept immovable. The result of calculation is illustrated by a numerical example.
The treatment throughout is made on the assumption that water is an incompressible, nonviscous fluid, and that the vibration amplitude is infinitesimally small.