Axially-moving materials arise in problems associated with spacecraft antennas, pipes conveying fluid and telescopic robotic manipulators. Flexible extendible beams are a special class of axially-moving materials, in which the axially-moving material is modelled as a slender beam and the mechanism of elastic deformation is transverse bending.
Hamilton's principle is used to derive the governing differential equation of motion and system invariant properties of a flexible extendible beam protruding from a rigid wall with prescribed extrusion profile. The mass of the system is not constant and the general analytical solution to the equation of motion is not known. In this study, numerical solutions are obtained using finite-element analysis. However, instead of following the obvious (but cumbersome) approach of using fixed-size elements and increasing their number, in a stepwise fashion, as mass elements enter the domain of interest, a more elegant approach is followed wherein the number of elements is fixed, while the sizes of the elements change with time. To this end, a variable-domain beam finite element whose size is a prescribed function of time is formulated.
The accuracy of this variable-domain beam element is demonstrated through the time-integration of equations of motion using various extrusion profiles. Additional verification is performed by the evaluation of the system's invariant quantities, comparison with a special analytical solution, and the dynamic stability analysis of pipes conveying fluid. The effects of wall flexibility, tip mass, and high-frequency axial-motion perturbations to the transverse response of the flexible extendible beam are also examined. In order to gain a deeper insight into the mechanics of this system, the dynamic stability characteristics of the flexible extendible beam are also investigated using various extrusion profiles. The effects of physical damping, tip mass, tip support and wall flexibility on the stability characteristics of this system are examined.
The power and versatility of this finite-element formulation is demonstrated in a simulation of an extruding flexible extendible beam which carries a tip mass and protrudes from a flexible envelope beam which imparts three-dimensional rigid-body rotations to the system. / Graduate
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/9598 |
| Date | 05 July 2018 |
| Creators | Stylianou, Marinos Costa |
| Contributors | Tabarrok, B. |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
| Rights | Available to the World Wide Web |
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