Volume 4, Issue 4
Influence of Gravity and Taper on the Vibration of a Standing Column

C. Y. Wang

Adv. Appl. Math. Mech., 4 (2012), pp. 483-495.

Published online: 2012-04

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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

Vibration, column, taper, weight.

  • AMS Subject Headings

74K10, 74H45, 74H55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-4-483, author = {}, title = {Influence of Gravity and Taper on the Vibration of a Standing Column}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {4}, pages = {483--495}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m11175}, url = {http://global-sci.org/intro/article_detail/aamm/132.html} }
TY - JOUR T1 - Influence of Gravity and Taper on the Vibration of a Standing Column JO - Advances in Applied Mathematics and Mechanics VL - 4 SP - 483 EP - 495 PY - 2012 DA - 2012/04 SN - 4 DO - http://doi.org/10.4208/aamm.10-m11175 UR - https://global-sci.org/intro/article_detail/aamm/132.html KW - Vibration, column, taper, weight. AB -

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.

C. Y. Wang. (1970). Influence of Gravity and Taper on the Vibration of a Standing Column. Advances in Applied Mathematics and Mechanics. 4 (4). 483-495. doi:10.4208/aamm.10-m11175
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