The equations governing torsional vibrations of unstiffened cylindrical tubes have been presented. Methods proposed in Part I are illustrated by considering the torsional vibrations of doubly symmetric tubes. An exact solution of a simply supported tube with the boundary of the cross section given by p=s/2π cos 2π S/S is presented. A free- free tube of rectangular cross section is analysed by using first order approximation equations and the results are in good agreement with earlier work
