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TECHNICAL PAPERS

Free Vibration of Helicoidal Beams of Arbitrary Shape and Variable Cross Section

[+] Author and Article Information
Wisam Busool

Structural Engineer, Nazareth-Reineh Village, 16940, Israele-maiil swis@tx.technion.ac.il

Moshe Eisenberger

Faculty of Civil Engineering, Technion Israel Institute of Technology, Technion City, Haifa 32000 Israele-mail: cvrmosh@techunix.technion.ac.il

J. Vib. Acoust 124(3), 397-409 (Jun 12, 2002) (13 pages) doi:10.1115/1.1468870 History: Received August 01, 2000; Revised September 01, 2001; Online June 12, 2002
Copyright © 2002 by ASME
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References

Wahl, A. M., 1963, Mechanical Springs, McGraw-Hill, New York.
Wittrick,  W. H., 1966, “On Elastic Wave Propagation in Helical Springs,” Int. J. Mech. Sci., 8, pp. 25–47.
Haktanir,  Vebil, 1995, “The Complementary Functions Method for the Element Stiffness Matrix of Arbitrary Spatial Bars of Helicoidal Axes,” Int. J. Numer. Methods Eng., 38, pp. 1031–1056.
Yildirim,  Vebil, 1999, “An Efficient Numerical Method for Predicting the Natural Frequencies of Cylindrical Helical Springs,” Int. J. Mech. Sci., 41, pp. 919–939.
Alghamdi,  S. A., Mohiuddin,  M. A., and Al-Ghamedy,  H. N., 1998, “Analysis of Free Vibration of Helicoidal Beams,” Engineering Computation, 15, pp. 89–102.
Yildirim,  Vebil, 1996, “Investigation of Parameters Affecting Free Vibration Frequency of Helical Springs,” Int. J. Numer. Methods Eng., 39, pp. 99–114.
Mottershead,  J. E., 1980, “Finite Elements for Dynamical Analysis of Helical Rods,” Int. J. Mech. Sci., 22, pp. 267–283.
Kosuke,  Nagaya and Takeda,  Sadahiko, 1986, “Free Vibration of Coil Springs of Arbitrary Shape,” Int. J. Numer. Methods Eng., 23, pp. 1081–1099.
Yildirim,  Vebil, 1997, “Free Vibration of Non-Cylindrical Coil Springs by Combined Use of the Transfer Matrix and the Complementary Functions Methods,” Communications in Numerical Methods in Engineering, 13, pp. 487–494.
Yildirim,  V., and Ince,  N., 1997, “Natural Frequencies of Helical Springs of Arbitrary Shape,” J. Sound Vib., 204, pp. 311–329.
Eisenberger,  Moshe, 1990, “Exact Static and Dynamic Stiffness Matrices for General Variable Cross Section Members,” AIAA J., 28, pp. 1105–1109.
Pearson,  D., 1982, “The Transfer Matrix Method for the Vibration of Compressed Helical Springs,” J. Mech. Eng. Sci., 24, pp. 163–171.
Xiong,  Y., and Tabarrok,  B., 1992, “A Finite Element Model for the Vibration of Spatial Rods Under Various Applied Loads,” Int. J. Mech. Sci., 34, pp. 41–51.

Figures

Grahic Jump Location
The 4th, 5th and 6th, mode shapes of cylindrical spring with clamped ends
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The 7th, 8th and 9th mode shapes of cylindrical staircase with variable cross-section, and both ends fixed
Grahic Jump Location
The 4th, 5th and 6th mode shape of cylindrical staircase with variable cross-section, and both ends fixed
Grahic Jump Location
The first three mode shapes of cylindrical staircase with variable cross-section, and both ends fixed
Grahic Jump Location
The 4th, 5th and 6th mode shape of hyperboloidal spring, with clamped ends
Grahic Jump Location
The first three mode shapes of hyperboloidal spring with clamped ends
Grahic Jump Location
The first three mode shapes of cylindrical spring with clamped ends
Grahic Jump Location
Geometry and degrees of freedom of a helical element in global coordinates
Grahic Jump Location
The different shapes of helical springs (a) cylindrical (b) barrel (c) conical (d) hyperboloidal

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