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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

Grant number: 13/18431-8
Support type:Scholarships in Brazil - Scientific Initiation
Effective date (Start): November 01, 2013
Effective date (End): October 31, 2014
Field of knowledge:Engineering - Mechanical Engineering - Mechanical Engineering Design
Principal Investigator:Marcos Silveira
Grantee:Arthur Nicolini Corazza
Home Institution: Faculdade de Engenharia (FE). Universidade Estadual Paulista (UNESP). Campus de Bauru. Bauru , SP, Brazil

Abstract

The aim of this project is to determine the nonlinear relationship between torsional rigidity and torsional end angle of a metalic 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 localisation 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 behaviour 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 smal scale rig, which enables the variation of the main parameters of the sysem. 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.