Determination of the natural frequencies and vibration modes of liquids in vessels of arbitrary shapes

A method is proposed for determining the natural frequencies and vibration modes of enclosed volumes of liquids wherein use is made of an iteration procedure for solving eigenvalue problems. The boundary-value problems arising at each step of the iteration are represented in curvilinear coordinates and solved using a finite-difference scheme. The accuracy and convergence of the method are evaluated by solving a series of test problems whose solutions are already known.