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Technical Briefs

Vibration of a Standing Heavy Column With Intermediate Support

[+] Author and Article Information
C. Y. Wang

Department of Mathematics, and Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824cywang@mth.msu.edu

J. Vib. Acoust 132(4), 044502 (Jul 15, 2010) (4 pages) doi:10.1115/1.4001511 History: Received July 26, 2009; Revised February 02, 2010; Published July 15, 2010; Online July 15, 2010

The vibration of a free standing column under its own weight is studied. An intermediate support increases the fundamental frequency. The optimum location for the support is determined for clamped-free, pinned-free, and sliding-free columns. The problem is integrated by a simple accurate initial value method. Approximate and exact relations are also found.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) The standing column with intermediate support. (b) An elemental segment

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Figure 2

C-F case. Normalized frequency parameter k versus support height b for various weight parameters β. The dashed curve is the locus of optimum locations.

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Figure 3

P-F case. Normalized frequency parameter k versus support height b for various weight parameters β. The dashed curve is the locus of optimum locations.

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Figure 4

S-F case. Normalized frequency parameter k versus support height b for various weight parameters β. The dashed curve is the locus of optimum locations.

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