Koiter,
W. T., 1996, “Unrealistic Follower Forces,” J. Sound Vib., 194, pp. 636–638.

Sugiyama,
Y., Langthjem,
M. A., and Ryu,
B. J., 1999, “Realistic Follower Forces,” J. Sound Vib., 225(4), pp. 779–782.

Bolotin, V. V., 1961, *Nonconservative Problems in the Theory of Elastic Stability*, Fizmatgiz Publishers, Moscow (in Russian) (English translation, Pergamon, New York, 1964).

Timoshenko, S. P., and Gere, J. M., 1963, *Theory of Elastic Stability*, McGraw–Hill, Auckland, p. 156.

Ziegler, H., 1968, *Principles of Structural Stability*, Waltham, MA.

Leipholz, H. H. E., 1980, *Stability of Elastic Systems*, Sijthoff and Noordhoff.

Dzhanelidze, G. Yu., 1958, “About Stability of a Column Under the Action of Follower Force,” *Proceedings of the Leningrad Polytechnic Institute*, No. 192, pp. 21–27 (in Russian).

Reut, V. I., 1939, “About the Theory of Elastic Stability,” *Proceedings of the Odessa Institute of Civil and Communal Engineering*, No. 1.

Nikolai, E. V., 1939, “About Criterion of Stability of Elastic Systems,” *Proceedings of the Odessa Institute of Civil and Communal Engineering*, No. 1 (in Russian).

Pflüger, A., 1950, *Stabilitätsprobleme der Elastostatik*, Springer-Verlag, Berlin, p. 217 (in German).

Euler,
L., 1778a, “Determinatio Onerum, Quae Columnae Gestare Valent,” Acta Acad. Sci. Petropolitanae, 1, pp. 121–145 (in Latin).

Euler,
L., 1778b, “Examen Insignis Puradoxi in Theoria Columnarum Occurentis,” Acta Acad. Sci. Petropolitanae, 1, pp. 146–162 (in Latin).

Panovko, Ya. G., and Gubanova, I. I., 1987, *Stability and Vibrations of Elastic Systems*, Nauka, Moscow, p. 131 (in Russian, 4th ed.).

Nikolai, E. V., 1955, *Works in Mechanics*, Gostekhizdat, Moscow, pp. 436–454 (in Russian).

Todhunter, I., and Pearson, K., 1886, *History of the Theory of Elasticity*, Cambridge University Press, Vol. 1, pp. 39–50.

Euler,
L., 1778c, “De Altitudine Columnarum Sub Proprio Pondere Corruentium,” Acta Acad. Sci. Petropolitanae, 1, pp. 163–193 (in Latin).

Feodosiev, V. I., 1950, *Selected Problems and Questions in Strength of Materials*, Gostekhizdat, Moscow, pp. 44, 183, and 184 (1st ed., in Russian).

Ziegler,
H., 1952, “Die Stabilitätskriterien der Elastomechanik,” Ingenieria, Mexico, 20(1), pp. 49–56.

Beck,
M., 1952, “Die Knicklast des Einseitig Eingespannten Tangential Gedrückten Stabes,” Z. Angew. Math. Phys., 3, pp. 225–228 (in German); 1952, 3, 476–477(E).

Beck,
M., 1955, “Knickung Gerader Staebe Durch Druck und Konservative Torsion,” Ingenieria, Mexico, 23, pp. 231–253 (in German).

Nemat-Nasser, S., 1973, *On Elastic Stability Under Nonconservative Forces*, University of Waterloo Press, Waterloo, Ontario, Canada.

Herrmann, G., 1971, “Dynamics and Stability of Mechanical Systems Under Follower Forces,” NASA CR-1782.

Dzhanelidze, G. Yu., 1965, “Stability of Elastic Systems Under Dynamic Loads,” *Problems of Stability in Structural Mechanics*, edited by V. V. Bolotin, I. M. Rabinovich, and A. F. Smirnov, Izdatelstvo Literatury po Stroitelstvu, Moscow, pp. 68–84 (in Russian).

Herrmann,
G., 1967, “Stability of Equilibrium of Elastic Systems Subjected to Non-conservative Forces,” Appl. Mech. Rev., 20, pp. 103–108.

Sundararajan,
C., 1975, “The Vibration and the Stability of Elastic Systems Subjected to Follower Forces,” Shock Vib. Dig., 7, pp. 89–105.

Bogach,
R., and Janishevsky
R., 1985, “Analysis and Synthesis of Columns, Compressed by Follower Forces, From the Stability Point of View,” Adv. Mech., 8(3), pp. 3–52 (in Russian).

Bolotin, V. V., 1995, “Dynamic Stability of Structures,” in *Nonlinear Stability of Structures*, A. N. Kounadis and W. B. Krätzig, eds., Springer-Verlag, Vienna, pp. 3–72.

Bolotin,
V. V., 1999, “Dynamic Instabilities in Mechanics of Structures,” Appl. Mech. Rev., 52(1), pp. R1–R9.

Langthjem,
M. A., and Sugiyama,
Y., 2000, “Dynamic Stability of Columns Subjected to Follower Loads: A Survey,” J. Sound Vib., 238(5), pp. 809–851.

Deineko,
K. S., and Leonov,
M. Ya., 1955, “Dynamic Method of Investigation of Stability of a Compressed Column,” PMM, 19, pp. 738–744 (in Russian).

Feodosiev, V. I., 1969, *Ten Lectures-Conversations on Strength of Materials*, Nauka, Moscow (in Russian).

Kounadis,
A. N., 1994, “On the Failure of Static Stability Analysis of Nonconservative Systems in Regions of Divergence Instability,” Int. J. Solids Struct., 31(15), pp. 2099–2120.

Plaut,
R., 1976, “Analysis of Nonconservative Elastic Systems,” J. Struct. Mech., 4, pp. 395–416.

Kounadis,
A. N., 1991, “On the Reliability of Postbuckling Analysis for Nonconservative Imperfect Systems,” Arch. Mech., 43(1), pp. 95–105.

Kounadis,
A. N., Avraam,
T., and Mallis,
J., 1992, “On the Reliability of Classical Divergence Instability Analysis of Ziegler’s Nonconservative Model,” Comput. Methods Appl. Mech. Eng., 95, pp. 317–330.

Kounadis,
A. N., 1997, “On Potential Dissipative Systems Exhibiting Periodic Attractors in Regions of Divergence,” Chaos, Solitons Fractals, 8(4), pp. 583–612.

Kounadis,
A. N., 1998, “Qualitative Criteria for Dynamic Buckling of Imperfection Sensitive Nonconservative Systems,” Int. J. Mech. Sci., 40(10), pp. 449–462.

Kounadis,
A. N., 2001, “Nonclassical Stability Problems: Instability of Slender Tubes Under Pressure,” J. Aerosp. Sci., 14(1), pp. 6–11.

Kounadis,
A. N., 1992, “On the Paradox of the Destabilizing Effect of Damping in Non-Conservative Systems,” Int. J. Non-Linear Mech., 27(4), pp. 597–609.

Kounadis, A. N., 2001, private comunication.

Lee,
G. E, and Reissner,
E., 1975, “Note on a Problem of Beam Buckling,” Z. Angew. Math. Phys., 26, pp. 839–841.

Neer,
A., and Baruch,
M., 1977, “Note on Static and Dynamic Instability of a Nonuniform Beam,” Z. Angew. Math. Phys., 28, pp. 735–740.

Dmitriyk,
W., 1992, “The Static Stability Problems of an Elastic Continuum Subjected to Follower-Type Loading,” Int. J. Solids Struct., 29(3), pp. 2545–2562.

Dmitriyk,
W., 1993, “Static Solutions of the Leipholz Problem,” Int. J. Solids Struct., 30(15), pp. 1997–2008.

Leipholz,
H. H. E., 1962, “Die Knicklast des Einseitig Eingespannten Stabes Mit Gleichmaessig Verteilter, Tangentialer Laengsbelastung (in German),” Z. Angew. Math. Phys., 6, pp. 581–589.

Harding, S., (ed.), 1976, *Can Theories Be Refuted*?, Kluwer, Dordrecht.

Lakatos, I., 1976, “Falsification and the Methodology of Scientific Research Programmes,” *Can Theories Be Refuted*?, S. Harding, ed., Kluwer, Dordrecht, pp. 205–247.

Willems,
N., 1966, “Experimental Verification of the Dynamic Stability of a Tangentially Loaded Cantilever Column,” J. Appl. Mech., 35, pp. 460–461.

Huang,
N. C., Nachbar,
W., and Nemat-Nasser,
S., 1967, “On Willems’ Experimental Verification of the Critical Load on Beck’s Problem,” J. Appl. Mech., 34, pp. 243–245.

Goldbaum, I. Ya., 1956, “Experimental Apparatus for Investigating of Stability of Elastic Column in Presence of Follower Force,” Diploma, Leningrad Polytechnic Institute (in Russian, quoted by G. Yu. Dzhanelidze, 1958).

Rzhanitsyn, A. R., 1955, *Stability of Equilibrium of Elastic Systems*, GITTL, Moscow (in Russian), pp. 161–162.

Yagn,
I. Yu., and Parshin,
L. K., 1966, “Experimental Study of Stability of a Column Compressed by a Follower Force,” Dokl. Akad. Nauk SSSR, 167(1), pp. 49–50 (in Russian).

Wood,
W. G., Saw,
S. S., and Saunders,
P. M., 1969, “The Kinetic Stability of a Tangentially Loaded Strut,” Proc. R. Soc. London, Ser. A, 313, pp. 239–248.

Pflüger,
A., 1955, “Zur Stabilität des Tangential Gedrückten Stabes,” Z. Angew. Math. Mech., 35(5) (in German).

Nemat-Nasser,
S., Prasad,
S. N., and Herrmann,
G., 1966, “Destabilizing Effect of Velocity-Dependent Forces in Nonconservative Continuous Systems,” AIAA J., 4, pp. 1276–1280.

Feldt,
W. T., Nemat-Naser,
S., Prasad
S. N., and Herrmann,
G., 1969, “Instability of a Mechanical System Induced by an Impinging Fluid Jet,” J. Appl. Mech., 36, pp. 693–701.

Qiu,
Z. L., and Nemat-Nasser,
S., 1985, “Instability of an Articulated Cantilever Induced by an Impinging Airjet,” Int. J. Solids Struct., 21(2), pp. 145–154.

Sugiyama,
Y., 1982, “Buckling of Generalized Reut Rod,” Solid Mechanics Archives, 7, pp. 433–466.

Sugiyama, Y., 1987, “Experiments On the Non-Conservative Problems of Elastic Stability,” Preprint ESP24.87035, 24th Annual Technical Meeting, Society of Engineering Science, (Sept. 20–23) Salt Lake City, Utah.

Mullagulov,
M. Kh., 1994, “Experimental-Theoretical Study of the Stability of Rods Compressed by Follower Forces,” Strength Mater., 26(6), pp. 441–446.

Anderson,
N. A., and Done,
G. T. S., 1971, “On the Partial Simulation of a Non-Conservative System by a Conservative System,” Int. J. Solids Struct., 7, pp. 183–191.

Xiong,
Y., Wang,
T. K., and Tabarrok,
B., 1990, “A Dynamic Method for Measuring the Critical Load of a Nonconservative Composite Column,” Dyn. Stab. Syst., 5(3), pp. 183–190.

Xiong,
Y., and Wang,
T. K., 1989, “On a Centripetally Loaded Model Simulating Beck’s Column,” Int. J. Solids Struct., 25(10), pp. 1107–1113.

Xiong, Y., 1995, Private communication, February 23.

Koiter, W. T., 1995, Private communication, February 20.

Sugiyama,
Y., Katayama,
T., Kirayama,
K., and Ryu,
B. J., 2000, “Experimental Verification of Dynamic Stability of Vertical Cantilevered Columns Subjected to a Subtangential Force,” J. Sound Vib., 236(2), pp. 193–207.

Sugiyama, Y., 1997, “Some Experimental Verifications of Nonconservative Stability Problems,” Seminar The Danish Center for Applied Mathematics and Mechanics, The Technical University of Denmark, August 15. (Copies of transparencies communicated by Professor Y. Sugiyama.)

Sugiyama,
Y., 2000, “Experimental Verification of Dynamic Instability of Vertical Cantilevered Columns Subjected to a Subtangential Force,” J. Sound Vib., 236(2), pp. 193–207.

Sugiyama, Y., Katayama, K., and Kinoi, S., 1990, “Experiment on Flutter of Cantilevered Columns Subjected to a Rocket Thrust,” *31st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference*, Paper AIAA-90-0948, Long Beach, pp. 1893–1898.

Sugiyama,
Y., Matsuike,
J., Ryu,
B. J., Katayama,
K., Kinoi,
S., and Enomoto,
N., 1995, “Effect of Concentrated Mass on Stability of Cantilevers Under Rocket Thrust,” AIAA J., 33, pp. 499–503; 34, pp. 212.

Sugiyama,
Y., Katayama,
K., Kirayama,
K., and Ryu,
B. J., 1999, “Experimental Verification of Dynamic Stability of Vertical Cantilevered Columns Subjected to a Sub-Tangential Force,” J. Sound Vib., 236(2), pp. 193–207.

Sugiyama,
Y., Katayama,
K., and Kinoi,
S., 1995, “Flutter of Cantilever Column Under Rocket Thrust,” J. Aerospace Eng., 8(1), pp. 9–15.

Done,
G. T. S., 1972, “Follower Force Instability of a Pod-Mounted Jet Engine,” Aeronaut. J., pp. 103–107.

Maier, G., 2000, private communication, November 8.

Karihaloo, B., 2001, private communication, April 4.

Karihaloo, B., 1969, “Stability of Some Non-Conservative Systems,” Ph.D. thesis, Moscow Civil Engineering Institute (in Russian).

Karihaloo, B., 2000a, private communication, November 14.

Karihaloo, B., 2000b, private communication, November 21.

Babitsky, V. I., 1999, private communication, January 5.

Babitsky,
V. I., and Chitayev,
M. Y., 1996, “Adaptive High-Speed Resonant Robot,” Mechatronics, 6(8), pp. 897–913.

Singer, J., Arbocz, J., and Weller, T., 1997, *Buckling Experiments*, 1 , pp. 1–3, Wiley, London (Vol. 2, 2002).

Smith,
T. E., and Herrmann,
G., 1972, “Stability of a Beam on an Elastic Foundation Subjected to a Follower Force,” J. Appl. Mech., 39, pp. 628–629.

Celep, Z., 1977, “On the Stability of a Column On an Elastic Foundation Subjected to a Non-Conservative Load,” *Proceedings of the Sixth National Science Congress*, The Scientific and Technical Research Council of Turkey, pp. 301–311.

Celep,
Z., 1980, “Stability of a Beam on an Elastic Foundation Subjected to a Nonconservative Load,” J. Appl. Mech., 47, pp. 111–120.

Sundararajan,
C., 1976, “Stability of Columns on Elastic Foundations Subjected to Conservative or Nonconservative Forces,” J. Sound Vib., 37, pp. 79–85.

Jacoby,
A., and Elishakoff,
I., 1986, “Discrete-Continuous Elastic Foundation May Leave the Flutter Load of the Pflüger Column Unaffected,” J. Sound Vib., 108, pp. 523–523.

Elishakoff,
I., and Wang,
X. F., 1987, “Generalization of Smith-Herrmann Problem With the Aid of Computerized Symbolic Algebra,” J. Sound Vib., 117(3), pp. 537–542.

Hauger,
W., and Wetter,
K., 1976, “Influence of an Elastic Foundation on the Stability of a Tangentially Loaded Column,” J. Sound Vib., 47(2), pp. 296–299.

Smith,
T. E., and Herrmann,
G., 1972, “Stability of a Beam on an Elastic Foundation Subjected to a Follower Force,” J. Appl. Mech., 39, pp. 628–629; Lee,
S. Y., and Yang,
C. C., 1994, “Nonconservative Instability of Non-Uniform Beams Resting on an Elastic Foundation,” J. Sound Vib., 169, pp. 433–444.

Parnes,
R., 1977, “A Paradoxical Case in Stability Analysis,” AIAA J., 15(10), pp. 1533–1534.

Zaslavsky,
A., 1979, “Increased Length May Enhance Buckling Load,” Isr. J. Technol., 17(3).

Zaslavsky,
A., 1981, “Discussion on Destabilizing Effect of Additional Restraint on Elastic Bar Structures,” Int. J. Mech. Sci., 23(6), pp. 383–384.

Panovko,
Ya. G., and Sorokin,
S. V., 1993, “The Paradoxical Influence of an Increase of Rigidity on Buckling Loads and Natural Frequencies for Elastic Systems,” Mech. Res. Commun., 20(1), pp. 9–14.

Voloshin,
I. I., and Gromov,
V. G., 1977, “On a Stability Criterion for a Bar on an Elastic Base Acted on by a Follower Force,” Mech. Solids, 12(4), pp. 148–150.

Wahed,
I. F. A., 1975, “The Instability of a Cantilever on an Elastic Foundation Under Influence of a Follower Force,” J. Mech. Eng. Sci., 33, pp. 219–222.

Anderson,
G. L., 1975, “The Influence of Rotary Inertia, Tip Mass and Damping on the Stability of a Cantilever Beam On an Elastic Foundation,” J. Sound Vib., 43, pp. 543–552.

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(1), pp. 103–118.

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(3), pp. 468–472.

Kar,
R. C., 1980, “Stability of a Nonuniform Viscoelastic Cantilever Beam On a Viscoelastic Foundation Under the Influence of a Follower Force,” Solid Mech. Archives, 4, pp. 457–473.

Lee,
H. P., 1996, “Dynamic Stability of a Tapered Cantilever Beam On an Elastic Foundation Subjected to a Follower Force,” Int. J. Solids Struct., 33(10), pp. 1409–1424.

Sinha,
S. C., and Pawlowski,
D. R., 1984, “Stability Analysis of a Tangentially Loaded Column with a Maxwell Type Viscoelastic Foundation,” Acta Mach., 52, pp. 41–50.

Voloshin,
I. I., and Gromov,
V. G., 1976, “Stability of Cantilevered Viscoelastic Bar Loaded by a Follower Force,” Mech. Solids, 11(4), pp. 157–161.

Sedov, L. I., 1980, *Thoughts About Science and About Scientists*, Nauka, Moscow (in Russian), p. 50.

Koiter,
W. T., 1985, “Elastic Stability,” Z. Flugwiss. Weltraumforsch., 9(4), pp. 205–210.

Leipholz,
H. H. E., 1988, “On the Occurrence of Non-Self-Adjointness in the Control of Elastic Structures,” Acta Mech., 73, pp. 95–119.

Doak, P. E., 1995, private communication, March 9.

Koiter,
W. T., 1980, “Buckling of a Flexible Shaft Under Torque Loads Transmitted by Cardan Joints,” Ingenieurs, 49, pp. 369–373.

Rzhanitsyn, A. R., 1966, “Stability of Nonconservative Systems with Two Degrees of Freedom,” *Proceedings of Second All-Union Congress on Theoretical and Applied Mechanics*, Jan. 30–Feb. 5, 1964, Nauka, Moscow (in Russian), Vol. 3, pp. 276–294.

Paı̈doussis,
M. P., 1987, “Flow-Induced Instabilities of Cylindrical Structures,” Appl. Mech. Rev., 40, pp. 163–175.

Paı̈doussis,
M. P., and Li
G. X., 1993, “Pipes Conveying Fluid: A Model Dynamical Problem,” J. Fluids Struct., 7, pp. 137–204.

Chen, S. S., 1987, *Flow-Induced Vibration of Circular Structures*, Hemisphere, Washington, DC.

Blevins, R. D., 1990, *Flow-Induced Vibrations*, Van Nostrand-Reinhold, New York.

Paı̈doussis, M. P., 1998, *Fluid-Structure Interaction, Slender Structures and Axial Flow*, Academic, London.

Herrmann,
G., and Nemat-Nasser,
S., 1967, “Instability Modes of Cantilevered Bars Induced by Fluid Flow Through Attached Pipes,” Int. J. Solids Struct., 3, pp. 39–52.

Nemat-Nasser,
S., and Herrmann,
G., 1966, “Torsional Instability of Cantilevered Bars Subjected to Non-Conservative Loading,” J. Appl. Mech., 33, pp. 102–121.

Bolotin, V. V., 1996, private communication, November 18.

Crandall,
S. H., 1995, “The Effect of Damping on the Stability of Gyroscopic Pendulums,” Z. Angew. Math. Phys., 46, special issue, S761–S780.

Paı̈doussis, M. P., 1986, “Flow-Instabilities of Cylindrical Structures,” *Proceedings of the 10th U.S. National Congress of Applied Mechanics*, J. P. Lamb, ed., pp. 155–170.

Leipholz, H. H. E., 1970, *Stability Theory*, Academic, New York.

Lamb,
H., 1908, Proc. R. Soc. London, Ser. A, 80, 168.

Sugiyama,
Y., and Paı̈doussis
M. P., 1981, “Studies on Stability of Two-Degree-of-Freedom Articulated Pipes Conveying Fluid: The Effect of Characteristic Parameter Ratios,” Theor Appl. Mech., 31, 333–342.

Zimmerman,
D. C., 2000, “Model Validation and Verification of Large and Complex Space Structures,” Inverse Probl., 8, pp. 93–118.

Inman,
D. J., and Minas,
C., 1990, “Matching Analytical Models With Experimental Data in Mechanical Systems,” Control and Dynamics Systems, 37, pp. 327–363.

Lottati,
I., and Kornecki,
A., 1986, “The Effect of Elastic Foundation and Dissipative Forces on the Stability of Fluid Conveying Pipes,” J. Sound Vib., 109, pp. 327–338.

Roth,
W., 1964, “Instabilitaet Durchstroemter Rohre,” Ingenieurs, 33, pp. 236–263 (in German).

Becker,
O., 1980, “Schwingungs-und Stabilitaets–Verhalten des Durchstroemten Rohres,” Kernenergie, 23, pp. 337–342 (in German).

Becker,
M., Hauger,
W., and Winzen,
W., 1978, “Exact Stability Analysis of Uniform Cantilevered Pipes Conveying Fluid or Gas,” Arch. Mech., 30, pp. 757–768.

Impollonia,
N., and Elishakoff,
I., 2000, “Effect of Elastic Foundation On Divergence and Flutter of an Articulated Pipe Conveying Fluid,” J. Fluids Struct., 14, pp. 559–573.

Elishakoff,
I., and Impollonia,
N., 2001, “Does a Partial Elastic Foundation Increase the Flutter Velocity of a Pipe Conveying Fluid?,” J. Appl. Mech., 68, pp. 206–212.

Benjamin,
T. B., 1961, “Dynamics of a System of Articulated Pipes Conveying Fluid: I Theory,” Proc. R. Soc. London, Ser. A, 261, pp. 487–499.

Gregory,
R. W., and Paı̈doussis,
M. P., 1966a, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid: II Experiments,” Proc. R. Soc. London, Ser. A, 293, pp. 512–527.

Djondjorov,
P. A., 2001, “Dynamic Stability of Pipes Partly Resting On Winkler Foundation,” J. Theor. Appl. Mech. (Sofia), 31(3), pp. 101–112.

Djondjorov,
P., Vassilev,
V., and Dzhupanov,
V., 2001, “Dynamic Stability of Fluid Conveying Cantilever Pipes On Elastic Foundations,” J. Sound Vib., 247(3), pp. 533–546.

Hauger,
W., and Vetter,
K., 1976, “Influence of an Elastic Foundation and the Stability of a Tangentially Loaded Column,” J. Sound Vib., 42, pp. 296–299.

Kacprzynski, J., and Kaliski, S., 1960, “Flutter of Deformable Rocket in Supersonic Flow,” *Proceedings of the 2nd International Congress in the Aerospace Sciences*, Zuerich, Sept. 12–16, pp. 911–925.

Glaser, R. F., 1965, “Vibration and Stability of Analysis of Compressed Rocket Vehicles,” NASA TN D-2533.

Feodosiev,
V. I., 1965, “On a Problem of Stability,” PMM, 2, pp. 391–392 (in Russian).

Beal,
T. R., 1965, “Dynamic Stability of s Flexible Missile Under Constant and Pulsating Thrusts,” AIAA J., 3, pp. 486–494.

Gopak,
K. N., 1960, “Loss of Stability by a Free Column That Moves Accelerating Under Follower Force,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Metall. Topl., No. 4 (in Russian).

Gopak,
K. N., 1970, “Stability of a Free Column Under Distributed Follower Force,” Prikl. Mekh., 6(7), pp. 116–118 (in Russian).

Kaliski,
S., and Solarz,
L., 1962, “Aeroelastic Vibration and Stability of Deformable Rotating Rocket in a Linearized Flow,” Proc. Vib. Probl., 3(1), pp. 57–68.

Kaliski,
S., and Woroszyl,
S., 1965, “Flutter of a Deformable Rocket in Supersonic Flow According to the Second Asymptotic Approximation,” Proc. Vib. Probl., 1(16), pp. 49–80.

Solarz,
L., 1969, “The Mechanism of the Loss of Stability of a Non-Guided Deformable Rocket,” Proc. Vib. Probl., 4(10), pp. 425–441.

Anderson, G. L., and Walter, W. W., 1976, “Qualitative Stability Characteristics of a Flexible Missile Subjected to a Circulatory Thrust,” *Proceedings of the 8th Southeastern Conference on Theoretical and Applied Mechanics*, Virginia Polytechnic Institute, pp. 379–389.

Mladenov,
K. A., and Sugiyama,
Y., 1997, “Stability of a Jointed Free-Free Beam Under End Rocket Thrust,” J. Sound Vib., 199, pp. 1–15.

Kirillov, O. N., and Seyranian, A. P., 1999, “Optimization and Stability of a Flying Column,” *Proceedings, of the 3rd World Congress of Structural and Multidisciplinary Optimization*, May 17–21, Buffalo, New York.

Chaudhry, Z., and Rogers, C. A., 1991, “Response of Composite Beams to an Internal Actuator Force,” Paper AIAA-91-1166-CP, pp. 186–193.

Tanaka, M., and Idehara, R., 1999, “Robust Shape Design of Non-Conservative Structural System With Piezoelectric Elements,” *Proceedings of the Third World Congress of Structural and Multidisciplinary Optimization*, May 17–21, Buffalo, New York.

Horikawa, H., June 1977, “Active Feedback Control of an Elastic Body Subjected to a Non-Conservative Force,” Ph.D. dissertation, Princeton University.

Wu,
J. J., 1976a, “Missile Stability Using Finite Elements–Unconstrained Variational Approach,” AIAA J., 14, pp. 313–319.

Wu,
J. J., 1976b, “On Missile Stability,” J. Sound Vib., 49(1), pp. 141–147.

Park,
Y. P., 1985, “Dynamic Stability of a Free-Free Timoshenko Beam Under Controlled Follower Force,” Proc. JSME Vibration Conference, 85, pp. 43–53.

Park,
Y. P., and Mote,
C. D., 1985, “The Maximum Controlled Follower Force On a Free-Free Beam Carrying a Concentrated Mass,” J. Sound Vib., 98(2), pp. 247–256.

Dzhupanov,
V. A., 2001a, “Twelve Methodical Notes On the Paradoxical Results in a Class of Dynamical Problems, Part 1,” J. Theor. Appl. Mech. (Sofia), 31(3), pp. 74–100.

Dzhupanov,
V. A., 2001b, “Twelve Methodical Notes On the Paradoxical Results in a Class of Dynamical Problems, Part 2,” J. Theor. Appl. Mech. (Sofia), 31(4), pp. 55–72.

Hetenyi, M., 1950, *Handbook of Experimental Stress Analysis*, 1st ed., Wiley, New York.

Drucker, D. C., 1968, “Thoughts on the Present and Future Interrelation of Theoretical and Experimental Mechanics,” *Experimental Mechanics, William M. Murray Lecture 1967*, 8 (3), pp. 97–106.

Drucker, D. C., 1962, “On the Role of Experiment in the Development of Theory,” *Proceedings of the 4th U.S. National Congress of Applied Mechanics*, ASME, New York, pp. 15–33.

Bolotin, V. V., 1971, “Stability of Viscoelastic Systems Subjected to Non-Conservative Forces,” *Instability of Continuous Systems*, edited by H. Leipholz, Springer, Berlin, pp. 349–360.

Herrmann, G., 2000, private communication, December 1.

Franklin, A., 1986, *The Neglect of Experiment*, Cambridge University Press, London.

Bažant, Z., and Celodin, L., 1991, *Stability of Structures*, Oxford University Press, New York.

Herrmann, G., 1971, “Determinism and Uncertainty in Stability,” in *Instability of Continuous Systems*, H. Leipholz, ed., Springer, Berlin, pp. 240–247.

Bolotin,
V. V., and Zhinzher,
N. I., 1969, “Damping and Stability of Elastic Systems Subjected to Non-Conservative Forces,” Int. J. Solids Struct., 5(9), pp. 965–989.

Walker,
J. A., 1972, “Mathematical Modeling of Discrete Nonconservative Dynamic Systems,” Int. J. Solids Struct., 18, pp. 249–259.

Devaney, R. L., 1989, *An Introduction to Chaotic Dynamical Systems*, Addison-Wesley, Reading.

Trefethen, L. N., 1998, “Maxims About Numerical Mathematics,” Computers, Science, and Life, SIAM News.

Ziegler, H., 1971, “Trace Effects in Stability,” in *Instability of Continuous Systems*, H. Leipholz, ed., Springer, Berlin, pp. 96–111.

Huang, N. C., 2001, private communication February 20.

Sugiyama, Y., 1998, private communication, June 16.

Bohn,
M. P., and Herrmann,
G., 1974b, “Instabilities of Spatial Systems of Articulated Pipes Conveying Fluid,” J. Fluids Eng., 96, pp. 289–296.

Rousselet,
J., and Herrmann,
G., 1977, “Flutter of Articulated Pipes of Finite Amplitude,” J. Appl. Mech., 44, pp. 154–157.

Rousselet,
J., and Herrmann,
G., 1981, “Dynamic Behavior of Continuous Cantilevered Pipes Conveying Fluid Near Critical Velocities,” J. Appl. Mech., 48, pp. 946–947.

Sugiyama,
Y., 1984, “Studies On Stability of Two-Degree-of-Freedom Articulated Pipes Conveying Fluid (The Effect of a Spring Support and Lumped Mass),” Bull. JSME, 27, No. 234, 2658–2663.

Sugiyama,
Y., and Noda,
T., 1981, “Studies On the Stability of Two-Degree-of-Freedom Articulated Pipes Conveying Fluid (Effect of an Attached Mass and Damping),” Bull. JSME, 24, No. 194, 1354–1362.

Seyranya,
A. P., 1990, “Destabilization Paradox in Stability Problems of Nonconservative Systems,” Adv. Mech., 13(2), pp. 89–124 (in Russian).

Kounadis,
A. N., 1983, “The Existence of Regions of Divergence Instability for Non-Conservative Systems Under Follower Forces,” Int. J. Solids Struct., 19(8), pp. 725–733.

Kounadis, A. N., 1995, “Nonlinear Dynamic Buckling and Stability of Autonomous Dissipative Discrete Structural Systems: Nonpotential Systems,” in *Nonlinear Stability of Structures*, edited by A. N. Kounadis and W. B. Krätzig, eds., Springer Verlag, Wien, pp. 143–168.

Jensen,
F., 1999, “Editorial: How to Succeed in Modeling,” Quality and Reliability Engineering, 15, p. 159.

Levanony,
D., and Baruch,
M., 1987, “Dynamic Stability of a NonUniform Beam Modeled in a Two-Degree-of-Freedom System,” Z. Angew. Math. Phys., 38, pp. 874–882.

Bismark-Nasr,
M. N., 1995, “Dynamic Stability of Shallow Shells Subjected to Follower Forces,” AIAA J., 33, pp. 335–360.

Baruch, M., 2001, private communication.

Bolotin, V. V., and Grigoliuk, E. I., 1976, “Review of Stability Theory,” *Mechanics in the SSSR in 50 Years*, Nauka, Moscow (in Russian).

Gorshkov,
A. G., and Shklyarchuk,
F. N., 1966, “Stability of an Elastic Body of Revolution in the Gas Flow Under the Action of a Follower Force,” Inzh. Zh. Mekh. Tverd. Tela, No. 5, pp. 151–154.

Dmitriyk, W., 1996a, “Two Buckling Modes of the Adjoint Static Instability of the Nonconservative Problems,” *Proceedings of the 26th Israel’s Mechanical Engineering Conference*, May 21–22, pp. 495–497.

Dmitriyk, W., 1996b, “Static Behavior of the Ziegler Pendulum,” *Proceedings of the 26th Israel’s Mechanical Engineering Conference*, May 21–22, pp. 209–211.

Gregory,
R. W., and Paı̈doussis,
M. P., 1966b, “Unstable Oscillation of Tubular Cantilevers Conveying Fluid. II. Experiments,” Proc. R. Soc. London, Ser. A, 293, pp. 528–542.

Paı̈doussis,
M. P., 1970, “Dynamics of Tubular Cantilevers Conveying Fluid,” J. Mech. Eng. Sci., 12, pp. 85–103.

Doak,
P. E., 1996, “Editor-in-Chief, Reply,” J. Sound Vib., 194(4), pp. 636–638.

Atanackovic, T. A., 1997, *Stability of Elastic Rods*, World Scientific, Singapore, p. 380.

Alfutov, N. A., 2000, *Stability of Elastic Structures*, Springer, Berlin, p. 120.

Sorensen, R. A., 1992, *Thought Experiments*, Oxford University Press, New York, p. 27.

Hempel, C., 1965, *Aspects of Scientific Explanation*, Free Press, New York, p. 165.

Mach, E., 1943, *Popular Scientific Lectures*, 5th ed., Open Court Publishers, La Salle, IL, p. 220.

Krinsky, Sh., 1970, “The Nature and Function of ‘Gedankenexperimente’ in Physics,” Ph.D. thesis, University of Michigan, pp. 22, 229.

Hiebert, E., 1974, “Mach’s Conception,” in *The Intersection Between Science and Philosophy*, Y. Elkana, ed., Humanities, Atlantic Highlands, NJ.

Yagn, Yu. I., and Parshin, L. K., 1967, “Experimental Study of Stability of a Bar Under Compression by a Follower Force,” *Proceedings of the Leningrad Polytechnic Institute*, 278 , pp. 52–54 (in Russian).

Faber, T. E., 1995, *Fluid Mechanics for Physicists*, Cambridge University Press, p. 161.

Lamb, Sir Horace, 1932, *Hydrodynamics*, 6th ed., Cambridge University Press (reprinted in 1993).

Sugiyama,
Y., Ryu,
S.-U., and Langthjem,
M. A., 2002, “Beck’s Column as the Ugly Duckling,” J. Sound Vib., 254(2), pp. 407–410.

Natke, H. G., and Cempel, C., 1997, *Model-Aided Diagnosis of Mechanical Systems*, Springer, Berlin, p. 8.

Popp, K., 1999, “Examples of Nonsmooth Mechanical Systems—An Overview,” *Proceedings, IUTAM Symposium on Unilateral Multibody Contacts*, F. Pfeiffer and Ch. Glockner, eds., Kluwer, Dordrecht, pp. 233–242.

Adali,
S., 1982, “Stability of a Rectangular Plate Under Nonconservative and Compressive forces,” Int. J. Solids Struct., 18(12), pp. 1043–1052.

Alfutov,
N. A., and Popov,
B. G., 1988, “Stability of a Self-Gravitating Bar,” Mech. Solids, 23(5), pp. 175–178.

Anderson,
G. L., 1972, “On the Role of the Adjoint Problem in Dissipative, Nonconservative Problems of Elastic Stability,” Meccanica, 7, pp. 165–173.

Augusti,
G., 1968, “Instability of Struts Subject to Radiant Heat,” Meccanica, 3(3), pp. 167–176.

Barta, J., 1971, “Examples of the Stabilizing and Destabilizing Effects,” in *Instability of Continuous Systems*, H. Leipholz, ed., Springer, Berlin, pp. 263–265.

Blottner,
F. G., 1990, “Accurate Navier–Stokes Results for the Hypersonic Flow Over a Spheric Nosetip,” J. Spacecr. Rockets, 27(2), pp. 113–122.

Bohn,
M. P., and Herrmann,
G., 1974, “The Dynamic Behavior of Articulated Pipes Conveying Fluid with Periodic Flow Rate,” J. Appl. Mech., 41, pp. 55–62.

Choset,
H., and Henning
W., 1999, “A Follow-the-Leader Approach to Serpentine Robot Motion Planning,” J. Aerospace Engineering, 12(2) pp. 65–73.

Dermendjian-Ivanova,
D. S., 1992, “Critical Flow Velocities of a Simply Supported Pipeline on an Elastic Foundation,” J. Sound Vib., 157(2), pp. 370–374.

Dermendjian-Ivanova, D. S., and Dzhupanov, V. A., 1990, “Analytical and Numerical Investigations of the Hydroelasticity of One-Span Pipes in Their Parameter Apace,” J. Theor. Appl. Mech. (Sofia), 21 (4 ), pp. 43–50 (in Bulgarian).

De Rosa,
M. A., Colangelo,
F., and Messina,
F., Colangelo,
F., 2003, “Dynamic Stability of Beams on Two-Parameter Elastic Soil Subjected to Partially Tangential Forces,” Mech. Res. Commun., 30, pp. 187–191.

Dmitriyk, W., 2001, “Hidden Solutions of Stability Problems,” *Proceedings of the 41st Israel’s Annual Conference of Aerospace Sciences*, February 21–22.

Doaré, O., and de Langre, E., 2002, “Effect of Length on the Instability of Hanging Pipes,” *Proceedings of FSI, AE &*FIV+N, November 17–22, Paper IMACE 2002-34018, New Orleans, Louisiana.

Doaré,
O., and de Langre,
E., 2002, “Local and Global Stability of Fluid-Conveying Pipes on Elastic Foundations,” J. Fluids Struct., 16(1), pp. 1–14.

Done,
G. T. S., 1973, “Damping Configurations That Have a Stabilizing Influence On Nonconservative Systems,” Int. J. Solids Struct., 9, pp. 203–215.

Duhem, P., 1976, “Physical Theory and Experiment,” *Can Theories Be Refuted?*, S. G. Hardling, ed., Reidel, Dordrecht, p. 1.

Dzhupanov, V. A., 2000, “Principle of Equal Presence in the Problem of the Dynamic Interaction of a Cantilever Pipe Conveying Fluid with Elasto-viscous Medium,” *Flow-Induced Vibration*, S. Ziada and Th. Staubli, eds., Balkema, Rotterdam, pp. 355–362.

Elishakoff, I., 2001, personal communication, 18 July.

Elishakoff,
I., and Jacoby,
A., 1987, “Influence of Various Types of Elastic Foundation On the Divergence and Flutter of Ziegler’s Model Structure,” Z. Angew. Math. Phys., 38, pp. 779–784.

Feodosiev,
V. I., 1984, “Some Unusual Examples of Equilibrium Stability of Elastic Systems,” Mech. Solids, 19(1), pp. 123–128.

de Finetti, B., 1974, *Theory of Probability: A Critical Introductory Treatment*, Wiley, New York.

Fung, Y. C., and Sechler, E. E., 1960, “Instability of Thin Elastic Shells,” *Structural Mechanics*, J. N. Goodier and N. J. Hoff, eds., Pergamon, New York, pp. 115–168.

Gladwell,
G. M. L., 1990, “Follower Forces: Leipholz’s Early Researches in Elastic Stability,” Basin Res., 17, pp. 277–286.

Glen, J., and Littner, G., eds., 1984, *A Dictionary of Mathematics*, Harper and Row, London, p. 130.

Goroshko, O. A., 1965, *Dynamics of Elastics Structure in Conditions of a Free Flight*, Naukova Dumka, Kiev (in Russian).

Hacking, I., 1983, *Representing and Intervening*, Cambridge University Press.

Hagedorn,
P., 1970, “On the Destabilizing Effect of Non-Linear Damping in Nonconservative Systems with Follower Forces,” Int. J. Non-Linear Mech., 5, pp. 341–358.

Herrmann,
G., and Nemat-Nasser,
S., 1967, “Instability Modes of Cantilevered Bars Induced by Fluid Flow Through Attached Pipes,” Int. J. Solids Struct., 3, pp. 39–52.

Herrmann, G., Nemat-Naser, S., and Prasad, S. N., 1966, “Models Demonstrating Instability of Non-Conservative Mechanical Systems,” Technical Report No. 66-4, The Technological Institute Department of Civil Engineering, Northwestern University.

Higuchi, K., 1992, “Experimental Study On Dynamic Instabilities of a Column Thrusted by Non-Conservative Forces,” Paper AIAA-92-2331-CP.

Horgan,
J., 1995, “From Complexity to Perplexity,” Sci. Am., 272(6), pp. 104–109.

Huseyin,
K., 1976, “Vibrations and Stability of Mechanical Systems,” Shock Vib. Dig., No. 8, 56–65.

Huseyin, K., 1978, *Vibrations and Stability of Multiple Parameter Systems*, International Publishing, Alphen aan den Rijin, p. 58.

Kalmbach,
C. F., Dowell,
E. H., and Moon,
F. C., 1974, “The Suppression of a Dynamic Instability of an Elastic Body Using Feedback Control,” Int. J. Solids Struct., 10, pp. 361–367.

Katayama, K., July 1997, “Experimental Verification of the Effect of Rocket Thrust on the Dynamic Stability of Cantilever Columns,” Ph.D. thesis, Osaka Prefecture University.

Katsitadze, O. I., 1970, “About Stability of Columns During the Dynamic Loading by Axial Follower Forces,” *Stroitelnaya Mekhanika i Raschet Sooruzhenii*, No. 2, pp. 76–77 (in Russian).

Kemp, P., 1997, *The Oxford Dictionary of Literary Quotations*, p. 114, Oxford University Press, Oxford.

Kirillov,
O. N., and Seyranian,
A. P., 2002, “Solution to the Hermann-Smith Problem,” Dokl. Phys., 47(10), pp. 767–771.

Kolkka,
R. W., 1984, “On the Non-Linear Beck’s Problem with External Damping,” Int. J. Non-Linear Mech., 14, pp. 497–505.

Konikow,
L. F., and Bredehoeft,
Y. D., 1992, “Grounduster Models Cannot be Validated,” Adv. Water Resour., 15, pp. 75–78.

Kordas,
Z., and Zyczkowski,
M., 1964, “On the Loss of Stability of a Rod Under a Super-Tangential Force,” Arch. Mech. Stosow, 15(1), pp. 7–31.

Kornecki,
A., 1973, “On the Character of Instability of Certain Aeroelastic Systems,” J. Appl. Mech., 40, pp. 616–617.

Kounadis,
A. N., 1977, “Stability of Elastically Restrained Timoshenko Cantilevers with Attached Masses Subjected to a Follower Force,” J. Appl. Mech., 44, pp. 731–736.

Kounadis,
A. N., and Simitses,
G. J., 1997, “Non-Conservative Systems with Syymmetrizable Stiffness Matrices Exhibiting Limit Cycles,” Int. J. Solids Struct., 32(3), pp. 315–529.

Lakatos, I., 1970, “Falsification and the Methodology of Scientific Research Programmes,” *Criticism of Growth of Knowledge*, I. Lakatos and D. Musgrave, eds., Cambridge University Press, Cambridge, pp. 91–196.

de Langre,
E., and Ouvrard,
A. E., 1999, “Absolute and Convective Bending Instabilities in Fluid Conveying Fluids,” J. Fluids Struct., 13, pp. 663–680.

Leijnse,
A., and Hassanizadeh,
S. M., 1994, “Model Definition and Model Validation,” Adv. Water Resour., 17, pp. 197–200.

Leipholz, H., 1975, *Die Direkte Methode der Variationsrechnung und Eigenwertprobleme der Technik*, edited by G. Braun, Karlsruhe, p. 175 (in German).

Leipholz, H. H. E., 1987, *Stability Theory*, Teubner, Stuttgart.

Lottati,
I., and Elishakoff,
I., 1987, “A New “Destabilization” Phenomenon: Influence of Rotary Damping,” Ingenieurs, 57, pp. 413–419.

Mahrenholtz,
O., and Boyact,
R., 1981, “On the Shape of Characteristic Curves for Optimal Structures Under Non-Conservative Loads,” Ingenieurs, 50, pp. 141–148.

Matsumoto,
G. Y., and Mote,
C. D., 1972, “Time Delay Instabilities in Large Order Systems with Controlled Follower Forces,” J. Dyn. Syst., Meas., Control, 39, pp. 330–334.

Menditto,
G., 1974, “Elastic Stability of a Uniform Cantilevered Beam on Elastic Foundation with a Shear Layer Subjected to a Follower Force,” Meccanica, 9(4), pp. 299–303.

Morgan,
M. R., and Sinha,
S. C., 1983, “Influencing of a Viscoelastic Foundation On the Stability of Beck’s Column: An Exact Analysis,” J. Sound Vib., 91(1), pp. 85–101.

Mottershead,
J. E., Ouyang,
H., Cartemell,
M. P., and Friswell,
M. I., 1997, “Parametric Resonances in an Annular Disc, With a Rotating System of Distributed Mass and Elasticity, and the Effects of Friction and Damping,” Proc. R. Soc. London, Ser. A, 453, pp. 1–19.

Nemat-Nasser, S., 1996, “Experimental Studies of Instability of Elastic Systems Subjected to Non-Conservative Loads” (private communication, October 7).

Oreskes,
N., Shrader-Frechetle,
K., and Belitz,
K., 1994, “Verification, Validation and Confirmation of Numerical Models in the Earth Sciences,” Science, 263, pp. 641–646, 4.

Paı̈doussis,
M. P., 1970, “Dynamics of Tubular Cantilevers Conveying Fluid,” J. Mech. Eng. Sci., 12(2), pp. 98–105.

Paı̈doussis,
M. P., 1992, “Calvin Rice Lecture: Some Curiosity Driven Research in Fluid Structure Interactions and Its Current Applications,” J. Pressure Vessel Technol., 115, pp. 2–14.

Paı̈doussis,
M. P., and Deksnis,
E. B., 1970, “Articulated Models of Cantilevers Containing Fluid: The Study of a Paradox,” J. Mech. Eng. Sci., 12, pp. 288–300.

Panovko,
Ya. G., and Sorokin,
S. V., 1987, “Quasi-Stability of Viscoelastic Systems with Follower Forces,” Mech. Solids, 2, pp. 128–132.

Panovko, Ya. G., 1985, *Mechanics of Deformable Solid Body*, Nauka, Moscow, pp. 43–51 (in Russian).

Parker, S. P., (ed.), 1984, *McGraw-Hill Dictionary of Scientific and Technical Terms*, 3rd ed., McGraw–Hill, New York, p. 1032.

Plaut,
R. H., 1993, “Comments On Critical Flow Velocities of a Simply Supported Pipeline on an Elastic Foundation,” J. Sound Vib., 168(3), p. 548.

Prasad,
S. N., and Herrmann,
G., 1969, “The Usefulness of Adjoint Systems in Solving Nonconservative Stability Problems of Elastic Continua,” Int. J. Solids Struct., 5, pp. 727–735.

Prasad,
S. N., and Herrmann,
G., 1970, “Stability of a Cantilevered Bar Subjected to a Transverse Follower Force of Fluid Jet,” Ingenieurs, 39(5), pp. 341–356.

Roache, P., 1998, *Verification and Validation in Computational Science and Engineering*, Hermosa Publishers, Albuquerque.

Ryu,
B. Y., and Sugiyama,
Y., 1994, “Dynamic Stability of Cantilevered Timoshenko Columns Subjected to a Rocket Thrust,” Comput. Struct., 51(4), pp. 331–335.

Sasou,
K., and Reason,
J., 1999, “Team Errors: Definition and Taxonomy,” Reliability Eng. Sys. Safety, 65, pp. 1–9.

Seyranyan,
A. P., 1994, “Collision of Eigenvalues in Linear Oscillatory Systems,” J. Appl. Math. Mech., 58(5), pp. 805–813.

Seyranyan,
A. P., 1996, “Stabilization of Nonconservative Systems By Deceptive Forces and Uncertainties in the Critical Load,” Phys. Dokl., 41(5), pp. 214–217.

Seyranyan, A. P., 2001, private communication (March).

Semler,
C., Alighanbari,
H., and Paı̈doussis,
M. P., 1998, “A Physical Explanation of the Destabilizing Effect of Damping,” J. Appl. Mech., 65, pp. 642–648.

Smith,
T. E., 1969, “Buckling of a Beam on a Wieghardt-Type Elastic Foundation,” Z. Angew. Math. Phys., 43, pp. 641–645.

Stein,
R. A., and Tobriner,
W. M., 1970, “Vibration of Pipes Containing Flowing Fluids,” J. Appl. Mech., 37, pp. 906–916.

Sugiyama, Y., 1983, “Stabilizing Effect of Damping on the Stability of Non-Conservative Systems Conveying Fluid,” Solid Mechanics Archives, 8 , 337–362.

Sugiyama,
Y., Kashima,
K., and Kawagoe,
H., 1976, “On an Unduly Simplified Model in the Non-Conservative Problems of Elastic Stability,” J. Sound Vib., 45, pp. 237–247.

Sugiyama,
Y., Katayama,
T., Kanki,
E., Nishino,
K., and Åkesson,
B., 1996, “Stabilization of Cantilevered Flexible Structures By Means of an Internal Flowing Fluid,” J. Fluids Struct., 10, pp. 653–661.

Sugiyama, Y., Ryu, S.-U., Hamatani, M., and Iwama, T., 2003, “Computational Approach to Damped Beck’s Column,” International Conference “Physics and Control,” Invited Session “Stability and Control Problems in Mechanics: Nonconservativeness, Bifunctions, Singularities” (Seyranian, A. P. and Kirillov, O. N., organizers).

Sundararajan,
C., 1973, “A Theorem on the Stability of Elastic Systems,” Z. Angew. Math. Phys., 24, pp. 287–290.

Sundararajan,
C., 1976, “Influence of an Elastic End Support On the Vibration and Stability of Beck’s Column,” Int. J. Mech. Sci., 18, pp. 213–241.

Sundararamaiah,
V., and Venkateswara,
Rao G., 1983, “Stability of Short Beck and Leipholz Columns On Elastic Foundations,” AIAA J., 21(7), pp. 1053–1054.

Tanaka, M., Tamura, K., and Idehara, R., 1997, “Optimization of Adaptive Beck’s Column With Piezoelectric Elements,” *Proceedings of the Second World Congress of Structural and Multidisciplinary Optimization*, W. Gutkovski and Z. Mroz, eds., Vol. 1 , pp. 399–404.

Tani,
J., and Sudani,
Y., 1995, “Active Flutter Surpresion of a Vertical Pipe Conveying Fluid,” JSME Int. J. Ser. C, 38(1), pp. 55–58.

Thompson, J. M. T., 1982, *Instabilities and Catastrophes in Science and Engineering*, Wiley, New York.

Thompson,
J. M. T., 1982, “‘Paradoxical’ Mechanics Under Fluid Flow,” Nature (London), 296, pp. 135–137.

Thomsen, J. J., 1997, *Vibrations and Stability*, McGraw–Hill, London.

Venkateswara Rao,
G., and Kanaka Raju,
K., 1982, “Stability of Tapered Cantilever Columns With an Elastic Foundation Subjected to a Concentrated Follower Force at the Free End,” J. Sound Vib., 81(1), pp. 147–151.

Walker,
J. A., 1978, “A Note On Stabilizing Damping Configurations for Linear Non-Conservative Systems,” Int. J. Solids Struct., 9(12), pp. 1543–1545.

Walter,
W. W., and Levinson,
M., 1968, “Destabilization of a Nonconservatively Loaded Elastic System Due to Rotary Inertia,” Can. Aeronaut. Space Institute, 1(2), pp. 91–93.

Webster, N., and Teall, E. N., 1984, *New Concise Webster’s Dictionary*, Modern Publishing, p. 210.

Wein, B., 2001, Intellectual honesty, *The Jerusalem Post International Edition*, November 30.

Xiong, Y., 1988, “Theoretical and Experimental Investigations On the Vibration and Stability of Non-Conservative Systems,” Ph.D. thesis, Beijing University (in Chinese).

Xiong,
Y., and Tabarrok,
B., 1993, “A Note On the Dynamic Behavior of Discretized Non-Conservative Systems,” J. Sound Vib., 162(3), pp. 429–439.

Xiong, Y., and Wang, T. K., 1987, “Stability of a Beck-Type Laminated Column,” *Proceedings of the Sixth International Conference of Composite Materials*, ICCM VI, England, 5 , 38–5.46.

Xiong,
Y., and Wang,
T. K., 1988, “A Centripetal-Load Model to Beck’s Column,” ACTA Aeronaut. Astronaut. Sinica, 9, pp. A.290–A293.

Ylken,
A., and Mikkola,
M., 1967, “A Beam On a Wieghardt-Type Elastic Foundation,” Int. J. Solids Struct., 3, pp. 617–633.

Ziegler, H., 1956, “On the Concepts of Elastic Stability,” in *Advances in Applied Mechanics*, Academic, New York, Vol. 4 , pp. 351–403.

Zorii,
L. M., and Chernukha,
Yu. A., 1971, “Influence of Supports On the Dynamic Stability of Elastic Column,” Prikl. Mekh., 7(2), pp. 134–136 (in Russian).