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Influence of Gravity and Taper on the Vibration of a Standing Column

Published online by Cambridge University Press:  03 June 2015

C. Y. Wang
C. Y. Wang*
Affiliation:
Departments of Mathematics and Mechanical Engineering, Michigan State University, East Lansing, MI 48824, USA
*
Corresponding author. Email: cywang@math.msu.edu
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Abstract

The stability and natural vibration of a standing tapered vertical column under its own weight are studied. Exact stability criteria are found for the pointy column and numerical stability boundaries are determined for the blunt tipped column. For vibrations we use an accurate, efficient initial value numerical method for the first three frequencies. Four kinds of columns with linear taper are considered. Both the taper and the cross section shape of the column have large influences on the vibration frequencies. It is found that gravity decreases the frequency while the degree of taper may increase or decrease frequency. Vibrations may occur in two different planes.

Keywords

74K1074H4574H55Vibrationcolumntaperweight
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 4 , August 2012 , pp. 483 - 495
Copyright
Copyright © Global-Science Press 2012

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