A supplementary, exact solution of an equivalent mechanical model for a sloshing fluid in a rectangular tank

In this paper and based on the linear potential theory of a fluid and an analogical approach, a supplementary, (complete) exact solution of an equivalent model is developed for a sloshing fluid in a rectangular tank and is compared with the existing solutions given by Graham and Rodriguez, Housner and a semi-analytical/numerical method. The results indicate that Graham and Rodriguez did not provide the correct location expressions for the convective masses. The expressions for the impulsive mass and its position given by Housner are not completely satisfactory approximations of the exact solutions. The solution in this paper can be an exact formulation to supplement the famous, traditional formulations given by Graham and Rodriguez as well as Housner.