Free‐Vibration Analysis of Tank Containing Two Liquids

Abstract

A study of the dynamic characteristics of rigidly supported upright circular cylindrical tanks containing two different liquids is presented. The governing differential equations for the tank—two‐liquid system are obtained by application of the Rayleigh‐Ritz procedure in combination with Lagrange's equation. The response functions examined include the fundamental natural frequency, the associated mode of vibration and hydrodynamic pressure exerted against the tank wall. Unlike the cases of tanks containing one liquid in which the dynamic response is controlled by four parameters, the dynamic response of a tank that contains two liquids is controlled by six parameters. The numerical results are presented in tabular and graphic forms, and are compared with those of the identical tank filled with one liquid. Also, a simple approximate equation for evaluating the fundamental natural frequency for preliminary design is proposed.