Natural oscillation shapes for a heavy fluid in an elliptic vessel

Abstract

Abstract The problem of constructing of shapes of the natural oscillations in a vertical cylindrical basin (vessel) with an elliptic cross-section in linearized form of an ideal incompressible fluid is considered. Only the gravity force is acting on the fluid. It is required to define the frequencies and shapes of the natural oscillations of the fluid as a function of the system’s parameters. The solution algorithm represented here is based on the method of separation of variables in elliptic coordinates, and the special developed method for the high-accuracy solution of the boundary problem. It used the variational principle and the procedure of continuation in the parameter. This approach shows its effectiveness and obtains the almost complete solution of the problem. For five lower oscillation modes, the natural shapes are determined with high degree of accuracy for a wide range of the eccentricity values.