MODAL PRECESSION OF A ROTATING HEMISPHERICAL SHELL

The purpose of this paper is to investigation the precession of vibrat ional modes (or standing waves) of a hemispherical shell due to the ef fect of a small constant axial rotation, where previously resonant mod es exists. Niordson thin shell theory, which allows the stretch of the middle surface and is expressed in an invariant form, is employed to derive the equations of bending vibration of a rotating open shell. An alysis is divided into two phases. For the first one, only the Corioli s force is considered. The frequency change due to the presence of Cor iolis force can be obtained by solving the equation of solvability con dition in the course of perturbation analysis. The precession rate of the vibrational modes is obtained in an analytical expression. For the second phase both the Coriolis and centrifugal forces are considered. The displacements are considered as the vectorial sum of the initial and incremental displacements. The initial displacements result from t he non-vibrational rotating shell which experiences centrifugal forces . The incremental displacements are the vibrational displacements of t he rotating shell relative to the initial state. Results through analy tical analysis show that the centrifugal force affects the frequencies of forward and backward travelling waves but does not influence the p recession rate of the vibrational modes. Copyright (C) 1996 Elsevier S cience Ltd.