Abstract
dc:description.abstractA second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, λ<sub>s</sub> + λ<sub>t</sub> <u>~</u>2Ï <sub>q</sub>, is examined. Second, the influence of an internal resonance, Ï <sub>q</sub =<u>~</u>3Ï r, on the previous case is studied. Finally, the effect of the internal resonance w<sub>r</sub><u>~</u>3w<sub>q</sub> on the resonance λ<sub>s</sub> + λ<sub>t</sub> <u>~</u>2Ï <sub>q</sub> is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of λ<sub>s</sub> + λ<sub>t</sub>.
Degree
thesis:*- Name thesis:degree_name
- Master of Science
- Level thesis:degree_level
- masters
- Discipline thesis:degree_discipline
- Engineering Mechanics
- Department dc:contributor.department
- Engineering Mechanics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 1988
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Gentry, Jeanette J.
- Chairs dc:contributor.committeechair
-
- Mook, Dean T.
- Plaut, Raymond H.
- Committee member dc:contributor.committeemember
-
- Nayfeh, Ali H.
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-06222010-020244
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/43402