Dynamic behavior of liquids in elastic tanks

Abstract

The finite element procedure is used in conjunction with a simple source distribution on all surfaces of a liquid, which is contained in a tank of virtually arbitrary geometry, to obtain expressions for the mass and stiffness (because of the gravity) matrices of the liquid. The accuracy of the formulation is evaluated by the numerical solution of eigenvalue problems appropriate to simple rigid tanks for which exact analytical solutions are available. Good agreement is obtained. Once the mass and stiffness matrices of the liquid are obtained, they can be combined with those of an elastic tank in order to study the dynamic behavior of liquids in elastic tanks. The matrices for the elastic tank can be generated by any of a variety of currently available finite element or finite difference programs. The dynamic behavior of a liquid in an elastic circular cylindrical tank is treated by making use of a standard finite element program. Very good agreement with the known exact analytical results is obtained. In addition, a tank geometry which cannot be readily analyzed by any of the previously available methods is considered.