Persistent Link:
http://hdl.handle.net/10150/202750
Title:
Waves on Elastic Rods and Helical Spring Problems
Author:
Durickovic, Bojan
Issue Date:
2011
Publisher:
The University of Arizona.
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.
Abstract:
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.
Type:
text; Electronic Dissertation
Keywords:
helices; rods; springs; waves; Applied Mathematics; compacton; elasticity
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Applied Mathematics
Degree Grantor:
University of Arizona
Advisor:
Goriely, Alain

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleWaves on Elastic Rods and Helical Spring Problemsen_US
dc.creatorDurickovic, Bojanen_US
dc.contributor.authorDurickovic, Bojanen_US
dc.date.issued2011-
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © 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.en_US
dc.description.abstractThis 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.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjecthelicesen_US
dc.subjectrodsen_US
dc.subjectspringsen_US
dc.subjectwavesen_US
dc.subjectApplied Mathematicsen_US
dc.subjectcompactonen_US
dc.subjectelasticityen_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineApplied Mathematicsen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorGoriely, Alainen_US
dc.contributor.committeememberTabor, Michaelen_US
dc.contributor.committeememberHausrath, Andrewen_US
dc.contributor.committeememberGoriely, Alainen_US
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