Variational Equation of Motion for Coupled Flexure and Torsion of Bars of Thin-Walled Open Section Including Thermal Effect

Abstract

Literature on flexure and torsion of bars of thin-walled open section is reviewed. The use of the variational equation of motion in solving problems of structural dynamics is further advocated. The variational equation of motion, together with the associated stress-displacement relations, is then derived for coupled flexure and torsion of the open section. Thermal effect is included, leading to a thermal twisting moment in addition to the usual thermal bending moments. For the special case of an open section with one axis of symmetry and with symmetrical heat input, only flexure is shown to be thermally inducible. The general result then reduces to the simple variational equation of flexural motion used in a separate study of the thermal flutter of a spacecraft boom.