Torsional Waves in Uniform Rods of non-Circular Section

Abstract

A differential equation for the torsional vibration of a uniform rod of non-circular section is derived which takes into account the longitudinal stress and inertia which arise from the warping of the cross-section. The boundary conditions relevant to the problem are also obtained. Curves showing the dispersion of torsional waves in rods of rectangular section as predicted by this theory are given and a comparison is made with the results of more simple torsion theories which either neglect the longitudinal stress and inertia effects or which take account of only one or other of them. Experimental resonance tests on rods of rectangular section for various side ratios are used as a basis of comparison with the theory for relatively long wavelengths and good agreement is found.