Coiling of elastic rods on rigid substrates
Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2014.
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Thesis |
| Language: | eng |
| Published: |
Massachusetts Institute of Technology
2015
|
| Subjects: | |
| Online Access: | http://hdl.handle.net/1721.1/93774 |
| _version_ | 1826208794564100096 |
|---|---|
| author | Khalid Jawed, Mohammad |
| author2 | Pedro M. Reis. |
| author_facet | Pedro M. Reis. Khalid Jawed, Mohammad |
| author_sort | Khalid Jawed, Mohammad |
| collection | MIT |
| description | Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2014. |
| first_indexed | 2024-09-23T14:12:25Z |
| format | Thesis |
| id | mit-1721.1/93774 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:12:25Z |
| publishDate | 2015 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/937742019-04-12T15:48:11Z Coiling of elastic rods on rigid substrates Khalid Jawed, Mohammad Pedro M. Reis. Massachusetts Institute of Technology. Department of Mechanical Engineering. Massachusetts Institute of Technology. Department of Mechanical Engineering. Mechanical Engineering. Thesis: S.M., Massachusetts Institute of Technology, Department of Mechanical Engineering, 2014. This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. Cataloged from student-submitted PDF version of thesis. Includes bibliographical references (pages 115-120). We investigate the deployment of a thin elastic rod onto a rigid substrate and study the resulting coiling patterns. In our approach, we combine precision model experiments, scaling analyses, and computer simulations towards developing predictive understanding of the coiling process. Both cases of deposition onto static and moving substrates are considered. We construct phase diagrams for the possible coiling patterns, e.g. meandering, stretched coiling, alternating loops, and translated coiling, and characterize them as a function of the geometric and material properties of the rod, as well as the height and relative speeds of deployment. The various modes selected and their characteristic length-scales are found to arise from a complex interplay between gravitational, bending, and twisting energies of the rod, coupled to the geometric nonlinearities intrinsic to their large deformations. We give particular emphasis to the first sinusoidal mode of instability, which we find to be consistent with a Hopf bifurcation, and rationalize the meandering wavelength and amplitude. Throughout, we systematically vary natural curvature of the rod as a control parameter, which has a qualitative and quantitative effect on the pattern formation, above a critical value that we determine. Upon establishing excellent quantitative agreement between experiments and simulations with no fitting parameters, we perform a numerical survey to relate the pattern size to the relevant length-scales arising from material properties and the setup geometry, and quantify the typical strain levels in the rod. The universality conferred by the prominent role of geometry in the deformation modes of the rod suggests using the gained understanding as design guidelines, in the original applications that motivated the study. These include the coiling of carbon nanotubes and the deployment of submarine cables and pipelines onto the seabed. by Mohammad Khalid Jawed. S.M. 2015-02-05T15:58:10Z 2015-02-05T15:58:10Z 2014 2014 Thesis http://hdl.handle.net/1721.1/93774 900649909 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 120 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mechanical Engineering. Khalid Jawed, Mohammad Coiling of elastic rods on rigid substrates |
| title | Coiling of elastic rods on rigid substrates |
| title_full | Coiling of elastic rods on rigid substrates |
| title_fullStr | Coiling of elastic rods on rigid substrates |
| title_full_unstemmed | Coiling of elastic rods on rigid substrates |
| title_short | Coiling of elastic rods on rigid substrates |
| title_sort | coiling of elastic rods on rigid substrates |
| topic | Mechanical Engineering. |
| url | http://hdl.handle.net/1721.1/93774 |
| work_keys_str_mv | AT khalidjawedmohammad coilingofelasticrodsonrigidsubstrates |