Waves on Elastic Rods and Helical Spring Problems

This work examines problems in the statics and traveling wave propagation on uniform elastic rods with constant curvature and torsion, i.e. a straight rod and a helical rod. The first set of problems concerns planar traveling loop-like waves on intrinsically straight rods. It is shown that loops with compact support can exist on homogeneous rods with a nonlinear constitutive relation, where the strain-energy density contains a quartic term. Next, the effect of heterogeneity in the material properties on the shape of the loop is examined using a homogenization method. The second set of problems deals with a system consisting of a helical spring with a force and a torque applied along the helix axis. First, an overview is presented of problems of finding the stresses given the strains, or vice-versa, assuming that the elastic parameters of the spring are known. Then, the inverse problem is examined, where both stresses and strains are measured, and optimal elastic parameters within the linear consitutive model are sought. Various forms of measured strains are considered. Finally, the special problem with zero axial torque is considered, and criteria when the spring overwinds with a tensile axial force applied are established.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Graduate College

Grantor dc:publisher

The University of Arizona.

Year dc:date.issued

2011

Author dc:creator

• Durickovic, Bojan

Advisor dc:contributor.advisor

• Goriely, Alain

Committee members dc:contributor.committeemember

• Tabor, Michael
• Hausrath, Andrew
• Goriely, Alain

• helices
• rods
• springs
• waves
• Applied Mathematics
• compacton
• elasticity

Statement dc:rights

• Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.

Language dc:language.iso

en

Handle dc:identifier.uri

http://hdl.handle.net/10150/202750

OAI identifier oai:identifier

oai:repository.arizona.edu:10150/202750