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TECHNICAL PAPERS

Does a Partial Elastic Foundation Increase the Flutter Velocity of a Pipe Conveying Fluid?

[+] Author and Article Information
I. Elishakoff

Department of Mechanical Engineering, Florida Atlantic University, Boca Raton, FL 33431 e-mail: ielishak@me.fau.edu

N. Impollonia

Dipartimento di Costruzioni e Tecnologie Avanzate, Universita di Messina, Contrada Sperone 98166, Italy

J. Appl. Mech 68(2), 206-212 (Aug 15, 2000) (7 pages) doi:10.1115/1.1354206 History: Received December 08, 1998; Revised August 15, 2000
Copyright © 2001 by ASME
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References

Smith,  T. E., and Herrmann,  G., 1972, “Stability of a Beam on an Elastic Foundation Subjected to a Follower Force,” ASME J. Appl. Mech., 39, pp. 628–629.
Sundararajan,  C., 1974, “Stability of Columns on Elastic Foundations Subjected to Conservative and Non-Conservative Forces,” J. Sound Vib., 37, No. 1, pp. 79–85.
Anderson,  G. L., 1976, “The Influence of a Wieghardt Type Elastic Foundation on the Stability of Some Beams Subjected to Distributed Tangential Forces,” J. Sound Vib., 44, No. 1, pp. 103–118.
Celep,  Z., 1980, “Stability of a Beam on Elastic Foundation Subjected to a Non-Conservative Load,” ASME J. Appl. Mech., 47, pp. 111–120.
Voloshin,  I. I., and Gromov,  V. G., 1977, “On a Stability Criterion for a Bar on an Elastic Base Acted on by a Following Force,” Mekhanika Tverdogo Tela (Mechanics of Solids), 12, No. 4, pp. 169–171.
Becker,  M., Hauger,  W., and Winzen,  W., 1977, “Influence of Internal and External Damping on the Stability of Beck’s Column on an Elastic Foundation,” J. Sound Vib., 54, No. 3, pp. 468–472.
Panovko, Ya. G., and Gubanova, S. V., 1987, Stability and Oscillations of Elastic Systems, Paradoxes, Fallacies and New Concepts, 4th Russian ed., Nauka Publishers, Moscow, pp. 131–132 (English translation of the first edition, 1965, Consultants Bureau, New York).
Koiter,  W. T., 1985, “Elastic Stability,” Z. Flugwiss. Weltraumforsch., 9, pp. 205–210.
Koiter,  W. T., 1996, “Unrealistic Follower Forces,” J. Sound Vib., 194, No. 4, pp. 636–638.
Herrmann,  G., 1967, “Stability and Equilibrium of Elastic Systems Subjected to Non-Conservative Forces,” Appl. Mech. Rev., 20, pp. 103–108.
Païdoussis,  M. P., and Li,  G. X., 1993, “Pipes Conveying Fluid: A Model Dynamical Problem,” Journal of Fluids and Structures, 7, pp. 137–204.
Paı̈dousis, M. P., 1998, Fluid-Structure Interaction, Academic Press, London.
Becker,  M., Hauger,  W., and Winzen,  W., 1978, “Exact Stability of Uniform Cantilevered Pipes Conveying Fluid or Gas,” Arch. Mech., 30, pp. 757–768.
Lottati,  I., and Kornecki,  A., 1986, “The Effect of an Elastic Foundation and of Dissipative Forces on the Stability of Fluid-Conveying Pipes,” J. Sound Vib., 109, No. 2, pp. 327–338.
Benjamin,  T. B., 1961, “Dynamics of a System of Articulated Pipes Conveying Fluid. I. Theory,” Proc. R. Soc. London, Ser. A, A261, pp. 457–486.
Gregory,  R. W., and Païdoussis,  M. P., 1966, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid. I. Theory,” Proc. R. Soc. London, Ser. A, A293, pp. 512–527.
Blevins, R. D., 1990, Flow Induced Vibrations, Van Nostrand Reinhold, New York, pp. 384–414.
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Figures

Grahic Jump Location
Forces and moments acting on elements of (a) a fluid and (b) the pipe
Grahic Jump Location
Dimensionless critical velocity νcr as a function of the attachment ratio α of a Winkler foundation with modulus χ1=200 and damping coefficient δ1=0.01, for different values of the mass ratio μ and of the internal damping (solid: γ=0; dotted: γ=0.001; dash-dotted: γ=0.005; dashed: γ=0.01). External damping β=0.001.
Grahic Jump Location
Dimensionless critical velocity νcr versus the attachment ratio α and the Winkler foundation modulus χ11=0.01). Internal damping γ=0.001; external damping β=0.001; mass ratio μ=0.1.
Grahic Jump Location
Dimensionless critical velocity νcr as a function of the attachment ratio α of a Winkler foundation with modulus χ1=50, for different values of the damping coefficients β and δ1. Internal damping γ=0.001; mass ratio μ=0.1.
Grahic Jump Location
Dimensionless critical velocity νcr as a function of the attachment ratio α of a rotatory foundation with modulus χ2=10 and damping coefficient δ2=0.01, for different values of the mass ratio μ and of the internal damping (solid: γ=0; dotted: γ=0.001; dash-dotted: γ=0.005; dashed: γ=0.01). External damping β=0.001.
Grahic Jump Location
Dimensionless critical velocity νcr versus the attachment ratio α and the rotatory foundation modulus χ22=0.01). Internal damping γ=0.001; external damping β=0.001; mass ratio μ=0.1.
Grahic Jump Location
Dimensionless critical velocity νcr as a function of the attachment ratio α of a rotatory foundation with modulus χ2=10, for different values of the damping coefficients β and δ2. Internal damping γ=0.001; mass ratio μ=0.1.
Grahic Jump Location
Dimensionless critical velocity νcr as a function of the attachment ratio α of a generalized foundation with moduli χ1=100,χ2 and damping coefficient δ1=0.01,δ2=0.01. Internal damping γ=0.001; external damping β=0.001; mass ratio μ=0.1.
Grahic Jump Location
Dimensionless critical velocity νcr as a function of the attachment ratio α of a generalized foundation with moduli χ1=100,χ2 and damping coefficient δ1=0.01,δ2=0.01. Internal damping γ=0.001; external damping β=0.001; mass ratio μ=0.5.

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