A typical failure in a heat exchanger is the breakdown of a tube due to impact-sliding wear. We investigate the dynamic behavior of a tube subjected to cross flow and study the stability of periodic solutions, bifurcations, and the route to chaos. The fluid-stiffness-controlled mechanism is chosen to represent the fluid forces and the impact forces are modeled by a piece-wise-Iinear spring. A two-point boundary-value algorithm is used to calculate periodic solutions and Floquet theory is used to study their stability. Poincare sections and bifurcation diagrams are used to study non-periodic solutions. Furthermore. for this autonomous system, the method of harmonic balance appears to be less suited than the two-point boundary-value algorithm for calculating periodic motions. For the case of a single-mode approximation. the results show that the tube undergoes relaxation oscillations and hence no bifurcations occur for fluid velocities ranging from 1.1 Ve to 3.0 Ve, where Ve is the critical fluid velocity. For the cases of two- and three-mode approximations. the results show that periodic solutions undergo bifurcations leading to chaos. Consequently. we conclude that chaos is the result of modal interactions. Observing the details of impacts. we also conclude that chaos appears when a second impact occurs on the same stopper. We also found intermittent chaos alternating with transient periodic motions. Lastly, we estimate the mean impact forces and mean impact-sliding wear work rates and compare them with previous results. / Master of Science
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/43786 |
| Date | 21 July 2009 |
| Creators | Yanna, Marc-Gabriel |
| Contributors | Engineering Mechanics, Nayfeh, Ali H., Johnson, Eric R., Mook, Dean T. |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Language | English |
| Detected Language | English |
| Type | Thesis, Text |
| Format | v, 97 leaves, BTD, application/pdf, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | OCLC# 28818420, LD5655.V855_1993.Y362.pdf |
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