Free vibration of elastically supported thin cylinders including gyroscopic effects

Abstract

The free vibration of thin cylinders with elastic boundary conditions was analysed by application of the exact solution of the Flugge shell theory equations of motion. The elastic boundaries were represented by distributed linear springs. By varying the eight spring constants any elastic or ideal boundary conditions can be simulated. The effect of flexibility in the boundary conditions for a cylinder supported at both ends and a cylinder supported at one end was determined for the lowest frequency vibration mode with two circumferential wavelengths as this mode is used in vibratory gyroscopes. It was found that the tangential stiffness has the greatest effect on the natural frequency of the cylinder supported at both ends while the axial boundary stiffness has the greatest influence on the natural frequency of the cylinder supported at one end. The effect of low rotation rates was also determined for these boundary conditions. It was found that the tangential stiffness of the boundaries has the largest effect on the sensitivity to rotation. The lowest frequency vibration mode with four circumferential wavelengths did not show the same trends A range of boundary stiffness for which analysis as an elastic boundary is essential was determine. Boundary stiffness out of this range may be regarded as zero (free) or infinite (rigid).