The theory of torsional vibrations of a four-boom thin-walled cylinder of rectangular cross-section

Abstract

The,torsional vibrations of a four-boom cylinder of doubiy symmetrical rectangular cross-section are considered and the differential equation of motion is derived on the assumption that the ribs maintain the section shape but do not themselves resist any warping out of their plane and that the walls of the cylinder are effective only in shear. Frequency equations are derived for a length of cylinder, free at both ends and prevented from rotating at the mid-section. The complete behaviour of the cylinder is determined by two non-dimensional parameters and curves are given from which the frequencies for any such cylinder may be determined. It is shown that the higher frequencies in particular may be underestimated by between 40 to 80 per cent if warping constraint effects are ignored. An approximate method is given for estimating the torsional frequencies of a cylinder with non-uniform characteristics.