Natural Frequencies of a Body of Revolution Vibrating Transversely in a Fluid

Abstract

IN A PREVIOUS PAPER [1]3 a procedure for determining the natural frequencies of a body vibrating in a fluid was described and applied to a flexible circular cylinder. A more practical and more difficult application of the method, to the case of a body of revolution, is presented in the present work. As was shown in [1], the natural frequencies are given by the eigenvalues of the potential energy matrix of the elastic body with respect to an inertia matrix, the latter being derived from the mass distribution of the body and the kinetic energy of the fluid. Thus two matrices must be obtained, and since the determination of the former is a problem in elasticity, and the determination of the latter one in hydrodynamics, these will be treated in separate sections. Then, in the final section, a particular body of revolution with prescribed elastic and inertial characteristics will be assumed, and its natural frequencies of vibration in air and in water will be calculated. For vibration in water, results obtained by means of strip theory and by the present matrix technique will be compared.