Modal precession of a rotating hemispherical shell

The purpose of this paper is to investigate the precession of vibrational modes (or standing waves) of a hemispherical shell due to the effect of a small constant axial rotation, where previously resonant modes 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. Analysis is divided into two phases. For the first one, only the Coriolis force is considered. The frequency change due to the presence of Coriolis force can be obtained by solving the equation of solvability condition 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 the non-vibrational rotating shell which experiences centrifugal forces. The incremental displacements are the vibrational displacements of the rotating shell relative to the initial state. Results through analytical analysis show that the centrifugal force affects the frequencies of forward and backward travelling waves but does not influence the precession rate of the vibrational modes. Copyright 0 1996 Elsevier Science Ltd.