General theory of cylindrical vibrations tubes. Part IV. Uncoupled torsional vibrations of open tubes

Abstract

Based on the ease in satisfying the free edge boundary conditio/I, open tubes are classified into two types, A and B. Type B tubes have more complicated free-edge boundary condition than that of type A tubes. An alternate formulation is evolved for type B tubes; this makes the free-edge boundary condition as simple as in type A tubes. A simply-supported open tube with the cross-section given by p=S/2π sin 2πS/S, is analysed exactly as well as by using approximation equations; errors in using the first order approximation equations are discussed. A simply-supported open tube of I-section, representative of type B tubes, is analysed by using first and second approximation equations .