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TECHNICAL BRIEFS

A Simple Formula for Evaluating the Fundamental Frequency Parameter of Initially Stressed Uniform Beams on Elastic Foundation

[+] Author and Article Information
G. Venkateswara Rao, R. Neetha

Structural Engineering Group, Vikram Sarabhai Space Centre, Trivandrum-695 022. India

J. Vib. Acoust 124(3), 451-454 (Jun 12, 2002) (4 pages) doi:10.1115/1.1467651 History: Received July 01, 2000; Revised January 01, 2002; Online June 12, 2002
Copyright © 2002 by ASME
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References

Hetenyi, M., 1961, Beams on Elastic Foundation, University of Michigan Press, Ann Arbor.
Timoshenko, S. P., and Gere, J. M., 1961, Theory of Elastic Stability, McGraw-Hill, New York.
Zhaohua,  F., and Cook,  R. D., 1983, “Beam Elements on Two Parameter Elastic Foundation,” J. Eng. Mech., 109(6), pp. 1390–1401.
Shastry,  B. P., and Rao,  G. V., 1986, “A Note on the Vibrations of a Short Cantilever Beam on Elastic Foundation,” J. Sound Vib., 111(1), pp. 176–178.
Eisenberger,  M., and Clastornik,  M., 1987a, “Vibration and Buckling of a Beam on a Variable Winkler Elastic Foundation,” J. Sound Vib., 115(2), pp. 233–241.
Eisenberger,  M., and Clastornik,  M., 1987b, “Beams on Variable Two Parameter Elastic Foundation,” J. Eng. Mech., 113(10), pp. 1454–1466.
Raju,  K. K., and Rao,  G. V., 1993, “Vibrations of Initially Stressed Beams and Plates Around Transition Values of Elastic Foundation Stiffness,” J. Sound Vib., 161(2), pp. 378–384.
Eisenberger,  M., 1994, “Vibration Frequencies for Beam on Variable One and Two Parameter Elastic Foundation,” J. Sound Vib., 176(5), pp. 577–584.
Naidu,  N. R., and Rao,  G. V., 1995, “Vibrations of Initially Stressed Uniform Beams on a Two Parameter Elastic Foundation,” Comput. Struct., 57(6), pp. 941–943.
Amba Rao,  C. L., 1967, “Effect of End Conditions on the Lateral Frequencies of Uniform Straight Columns,” J. Acoust. Soc. Am., 42(2), pp. 900–901.
Galef,  A. E., 1968, “Bending Frequencies of Compressed Beams,” J. Acoust. Soc. Am., 44(8), pp. 643.
Bokain,  A., 1988, “Natural Frequencies of Beams Under Compressive Axial Loads,” J. Sound Vib., 26(1), pp. 49–65.
Karnovsky, I. A., and Lebed, O. I., 2001, Formule for Structural Dynamics: Tables, Graphs and Solutions, McGraw Hill, Inc., pp. 299–304.
Gorman,  D. J., 2000, “Free Vibration and Buckling of Inplane Loaded Plates with Rotational Edge Support,” J. Sound Vib., 229(2), pp. 755–773.
Leissa, A. W., 1969, Vibration of Plates, NASA SP-160.

Figures

Grahic Jump Location
Beam on elastic foundation with compressive load P
Grahic Jump Location
A Uniform beam with end elastic rotational restraints under axial compression
Grahic Jump Location
A square plate under uniaxial compression

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