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: 14/04768-3
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: August 11, 2014
• End date: December 29, 2014
• Field of knowledge: Engineering - Mechanical Engineering - Mechanics of Solids
• Principal Investigator: Marcos Silveira
• Grantee: Marcos Silveira
• Visiting researcher: Pankaj Wahi
• Visiting researcher institution: Indian Institute of Technology, Kanpur (IIT KANPUR), India
• 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 stiffness and torsion angle of an elastic beam confined in a cylinder, and to use this relationship for the dynamical analysis of a system with torsional oscillations. Helical bucking of an elastic beam in contact with a cylindrical confinement is present in many areas of science. It is of great importance for oil industry, in which the long and slender drill-strings are axially loaded and twisted. The helix inside a cylinder became a recurring problem in advanced continuum mechanics, as it exhibits complex nonlinear phenomena of localization and chaos. In a recent work it was observed that the helical configuration is consequence of the torsional load alone, which confirms that there exists a different path to helical buckling which is not related to sinusoidal buckling, stressing the importance of the geometrical behavior of the beam. Therefore, it is interesting to determine the nonlinear relationship between torsional stiffness and torsion angle of an elastic beam confined in a cylinder. The objective is divided in two parts. On the first part, the nonlinear relationship between torsional stiffness and torsion angle of such elastic beam will be determined experimentally, with the use of a small-scale rig. On the second part, this relationship will be included on the model of torsional stiffness for the analysis of a system with torsional oscillations, similar to the one discussed by Silveira & Wiercigroch (2009) and Silveira (2011), using usual methods in nonlinear dynamics, such as bifurcation diagrams and basins of attraction, in order to identify regions in which undesirable phenomena may occur. The host researcher knows the visiting researcher, Pankaj Wahi, named for this project, from his stay in the University of Aberdeen, between 2008 and 2011, while he was working on his PhD degree, and the visiting researcher made several visits related to research projects in common. As a consequence of this collaboration, there is great interest in developing joint projects, involving research groups from UNESP Bauru and IIT Kanpur, including researchers and students, with a view to promote this collaboration. It is expected that the knowledge of Dr Pankaj Wahi over the subjects related to this project may contribute to further development of the analyses of the experimental and numerical results obtained from the research project during the visit. Specialized techniques of analysis of dynamical systems presenting stick-slip oscillations are extensively used by the visiting researcher in his projects, and some of the experience with such techniques may be transmitted to the local research group through the daily contact, and more specifically through the short courses which the visiting researcher will offer. In general terms, the visit will further promote the interaction between research groups from UNESP Bauru and IIT Kanpur, enabling the cooperation between researchers and students in projects related to the research areas in common, including analytical, experimental and numerical methods applied to the dynamical analysis of mechanical systems, such as impact systems, impact absorbers, energy harvesting, and control systems. (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, M.; WAHI, P.; FERNANDES, J. C. M.. Exact and approximate analytical solutions of oscillator with piecewise linear asymmetrical damping. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, v. 110, p. 115-122, APR 2019. (14/04768-3)

SILVEIRA, M.; WAHI, P.; FERNANDES, J. C. M.. Effects of asymmetrical damping on a 2 DOF quarter-car model under harmonic excitation. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 43, p. 14-24, FEB 2017. (14/04768-3)