Free Vibration of a High Speed Rotating Truncated Spherical Shell

Abstract

This paper is the first work on the vibration of a highspeed rotating spherical shell that rotates about its symmetric axis by developing a set of motion governing equations with consideration of both the Coriolis and centrifugal accelerations as well as the hoop tension arising in the rotating shell due to the angular velocity. To the author's understanding, no such work has so far been published on the rotating spherical shell with the Coriolis and centrifugal accelerations as well as the hoop tension, although there have been the works published on the rotating hemispherical shell with consideration of the Coriolis and centrifugal forces. A thin rotating isotropic truncated circular spherical shell with the simply supported boundary conditions at both the ends is taken as an example for the free vibrational analysis. In order to validate the present formulation, comparisons are made with a nonrotating isotropic spherical shell, and a good agreement is achieved since no published data results from open literature are available for comparison on the dynamics of rotating spherical shell. By the Galerkin method, several case studies are conducted for investigation of the influence of the important parameters on the frequency characteristics of the rotating spherical shell. The parameters studied include the circumferential wave number, the rotational angular velocity, Young's modulus of the shell material, and the geometric ratio of the thickness to radius of the spherical shell.