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.
Issue Section:
Technical Briefs
Keywords:
initial value problems,
shapes (structures),
vibrations,
column,
vibration,
heavy,
support
1.
Huang
, T.
, and Dareing
, D. W.
, 1969, “Buckling and Frequencies of Long Vertical Pipes
,” J. Engrg. Mech. Div.
0044-7951, 95
, pp. 167
–181
.2.
Paidoussis
, M. P.
, and Maisons
, P. E. T.
, 1971, “Free Vibration of a Heavy Damped, Vertical Cantilever
,” ASME J. Appl. Mech.
0021-8936, 38
, pp. 524
–526
.3.
Naguleswaran
, S.
, 2004, “Transverse Vibration of a Uniform Euler-Bernoulli Beam Under Linearly Varying Axial Force
,” J. Sound Vib.
0022-460X, 275
, pp. 47
–57
.4.
Virgin
, L. N.
, Santillan
, S. T.
, and Holland
, D. B.
, 2007, “Effect of Gravity on the Vibration of Vertical Cantilevers
,” Mech. Res. Commun.
0093-6413, 34
, pp. 312
–317
.5.
Barasch
, S.
, and Chen
, Y.
, 1972, “On the Vibration of a Rotating Disk
,” ASME J. Appl. Mech.
0021-8936, 39
, pp. 1143
–1144
.6.
Wang
, C. M.
, Wang
, C. Y.
, and Reddy
, J. N.
, 2005, Exact Solutions for Buckling of Structural Members
, CRC
, Boca Raton, FL
.7.
Pilkington
, D. F.
, and Carr
, J. B.
, 1970, “Vibration of Beams Subjected to End and Axially Distributed Loading
,” J. Mech. Eng. Sci.
0022-2542, 12
, pp. 70
–72
.8.
Courant
, R.
, and Hilbert
, D.
, 1955, Methods of Mathematical Physics
, Vol. 1
, Interscience
, New York
, Chap. 5.Copyright © 2010
by American Society of Mechanical Engineers
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