On Vibration of a Rectangular Tank filled with Water-V

Abstract

When side-walls of a rectangular tank, which is filled with water, are vibrating, the inside water will also make 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 IV, of the same title, the author has made a theoretical study on the value of “virtual mass” of water, and examined various factors which affect the value of virtual mass. In the present report, which is the continuation of the same study, the case is examined wherein two opposite (rectangular) side-walls have different values of flexural rigidity. The approximate formula for the fundamental frequency of free-vibration of the system (consisting of rectangular plates and water) is given. Also, some numerical examples which show us the effect of different values of flexural rigidity of side-walls to fundamental frequency of the system, are also given. The treatment throughout is made on the assumption that water is an incompressible, non-viscous fluid, and that the vibration amplitude is infinitesimally small.