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| Document Title |
An Analysis of the Fundamental Vibrations of Non-Convex Shapes
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| Type of Resource |
still image
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| Date Created |
2009-05-12
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| Digital Origin |
born digtal
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| Rights Statement |
http://digital.uwyo.edu/copyright.htm
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| Keyword (topic) |
drum head
non-convex
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| Series Title |
Undergrauate Research Day 2009
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| Creator(s) |
Anderson, Nick
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| Contributor(s) |
Selden, Dr. Jeff
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| Publisher |
University of Wyoming
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| Place of publication |
Laramie, Wyoming
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| Language |
eng
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| Summary |
The vibrations of a drum head can be understood as being built up from more basic vibrations and the specific point which “travels” the farthest on the drum is called the maximum. Much is known about the properties of maximum when we consider drum heads that are convex, but when we force the drum head into a shape that is no longer convex there is very little known about the properties governing this maximum. This research project has been concerned with analyzing this maximum within non-convex shapes through the use of differential equations and computer modeling software, in order to better understand the principles behind this maximum. This is accomplished by initially modeling convex shapes through software such as Matlab or FlexPDE, and then analyzing the behavior of the maximum as these shapes are forced into being non-convex. An example of this is a 1 by 2 rectangle, which is then forced into being more of an H shape. This data will be contributed back to the mathematical community, as there is a lack of information in this field currently, with the hope being that further research will be conducted in this field of mathematics.
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| Notes |
From - Undergraduate Research Day 2009 - Celebration of Research - Abstracts
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