Determination of the nonlinear relationship between torsional stiffness and torsional angle of an elastic slender beam confined inside a cylinder, with fixed and free ends

Abstract

The aim of this project is to determine the nonlinear relationship between torsional rigidity and torsional end angle of a metallic beam confined in a cylinder, and to use this relationship for the analysis of the dynamics of a system with torsional oscillations. The helical buckling of an elastic beam confined in a cylinder is present in many areas of science. It is of great importance for the oil industry, where long and slender drill-strings are axially loaded and twisted simultaneously. It is also important for the positioning of cateters in patients with cardiac problems, when a guide-wire is inserted inside a human artery. Even the conformation and functioning of DNA molecules are related to this type of buckling. Therefore, the helix inside a cylinder became a recurrent problem in advanced continuum mechanics, as it exhibits complex nonlinear phenomena of localization and chaos. A recent study showed that the formation of the helical configuration is a result of only the torsional load, confirming that there is a different path to helical buckling which is not related to the sinusoidal buckling, stressing the importance of the geometrical behavior of the beam. Thus, it is interesting to determine the nonlinear relationship between the torsional rigidity and torsional end angle of a beam confined in a cylinder. This relationship will be obtained experimentally with a small scale rig, which enables the variation of the main parameters of the system. The relationship will be used for the analysis of the dynamics of a system with torsional oscillations, with the use of numerical methods applied to nonlinear dynamics.