Experimental determination of the nonlinear relationship between torsional rigidity and torsional angle for dynamic analysis of an elastic slender beam confined inside a cylinder

• Grant number: 12/19774-3
• Support Opportunities: Regular Research Grants
• Start date: January 01, 2013
• End date: December 31, 2014
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Principal Investigator: Marcos Silveira
• Grantee: Marcos Silveira
• Host 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 an elastic 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. A hardening characteristic should be present, as the effects of torsion and bending are coupled. The results obtained experimentally with a smal scale rig will be used to determine this characteristic, which 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 such as bifurcation diagrams and basins of attraction, in order to determine regions where undesirable phenomena may occur. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

SILVEIRA, MARCOS; GONCALVES, PAULO J. P.; BALTHAZAR, JOSE M.. MULTI-CORE AND MANY-CORE SPMD PARALLEL ALGORITHMS FOR CONSTRUCTION OF BASINS OF ATTRACTION. Journal of Theoretical and Applied Mechanics, v. 57, n. 4, p. 1067-1079, 2019. (12/19774-3)