Dual series solutions in composite domain pertaining to torsion of cylinders

The torsion of two finite, coaxial, circular cylinders of the same radius in perfect adhesion is considered. A part of the cylincrical surface of the system is held fixed against rotation while the remaining part is traction free. Torque is applied by means of a rigidly attached disc at one of the ends. The present mixed boundary value problem is formulated in terms of certain eigenfunctions pertaining to the composite domain. Appropriate form of the orthogonality of the eigenfunctions is given which is employed to reduce the dual series extending over the two regions to the solution of a Fredholm integral equation of the second kind. This is accomplished by means of an extension of the well known method of solving dual series due to Sneddon and Srivastav. Based upon the numerical solution of the integral equations, quantities of practical interest are graphically shown.