Controversy Associated With the So-Called “Follower Forces”: Critical Overview

[1]  Peter Hagedorn,et al.  On the destabilizing effect of non-linear damping in non-conservative systems with follower forces , 1970 .

[2]  T. Tarnai,et al.  Destabilizing effect of additional restraint on elastic bar structures , 1980 .

[3]  Vladimir I. Babitsky,et al.  Adaptive high-speed resonant robot , 1996 .

[4]  W. Dmitriyuk,et al.  The static stability problems of an elastic continuum subjected to follower-type loading , 1992 .

[5]  G.T.S. Done,et al.  Damping configurations that have a stabilizing influence on nonconservative systems , 1973 .

[6]  Michael P. Païdoussis,et al.  Flow-induced Instabilities of Cylindrical Structures , 1987 .

[7]  Sarp Adali,et al.  Stability of a rectangular plate under nonconservative and conservative forces , 1982 .

[8]  Sia Nemat-Nasser,et al.  On Willems’ Experimental Verification of the Critical Load in Beck’s Problem , 1967 .

[9]  Raymond H. Plaut,et al.  Comments on "Critical Flow Velocities of a Simply Supported Pipeline on an Elastic Foundation" , 1993 .

[10]  Robert W. Kolkka,et al.  On the non-linear Beck's problem with external damping , 1984 .

[11]  Mikael A. Langthjem,et al.  BECK'S COLUMN AS THE UGLY DUCKLING , 2002 .

[12]  S. Nemat-Nasser,et al.  Destabilizing effect of velocity-dependent forces in nonconservative continuous systems Technical report no. 65-4 , 1965 .

[13]  Martti Mikkola,et al.  A beam on a wieghardt-type elastic foundation , 1967 .

[14]  J. A. Walker.  A note on stabilizing damping configurations for linear nonconservative systems , 1973 .

[15]  Z. Celep.  Stability of a Beam on an Elastic Foundation Subjected to a Nonconservative Load , 1980 .

[16]  M. P. Bohn,et al.  The dynamic behavior of articulated pipes conveying fluid with periodic flow rate. , 1974 .

[17]  Hans Günther Natke,et al.  Model-aided diagnosis of mechanical systems , 1996 .

[18]  I. Lakatos.  Falsification and the Methodology of Scientific Research Programmes , 1976 .

[19]  H. Ziegler.  Principles of structural stability , 1968 .

[20]  Sen-Yung Lee,et al.  Non-Conservative Instability of Non-uniform Beams Resting on an Elastic Foundation , 1994 .

[21]  Anthony N. Kounadis.  The existence of regions of divergence instability for nonconservative systems under follower forces , 1983 .

[22]  Menahem Baruch,et al.  Dynamic instability of a non-uniform beam modeled in a two-degree-of-freedom system , 1987 .

[23]  C. Wright.  Representing and Intervening , 1985 .

[24]  Anthony N. Kounadis,et al.  Nonclassical Stability Problems: Instability of Slender Tubes under Pressure , 2001 .

[25]  E. Reissner,et al.  Note on a problem of beam buckling , 1975 .

[26]  K. N. Gopak.  Stability of a free beam with a distributed following load , 1970 .

[27]  M. Païdoussis,et al.  Unstable oscillation of tubular cantilevers conveying fluid I. Theory , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[28]  E. de Langre,et al.  ABSOLUTE AND CONVECTIVE BENDING INSTABILITIES IN FLUID-CONVEYING PIPES , 1999 .

[29]  Howie Choset,et al.  A Follow-the-Leader Approach to Serpentine Robot Motion Planning , 1999 .

[30]  V. V. Bolotin,et al.  Effects of damping on stability of elastic systems subjected to nonconservative forces , 1969 .

[31]  Chelliah Sundararajan.  A theorem on the stability of elastic systems , 1973 .

[32]  Donald R Pawlowski,et al.  Stability analysis of a tangentially loaded column with a maxwell type viscoelastic foundation , 1984 .

[33]  Oleg N. Kirillov,et al.  Solution to the Herrmann-Smith problem , 2002 .

[34]  W Dmitriyuk,et al.  Static solutions of the leipholz problem , 1993 .

[35]  V. V. Bolotin.  Stability of Viscoelastic Systems Subjected to Nonconservative Forces , 1971 .

[36]  Yoshihiko Sugiyama.  Studies on Stability of Two-degree-of-freedom Articulated Pipes Conveying Fluid : The Effect of a Spring Support and a Lumped Mass , 1984 .

[37]  Sia Nemat-Nasser,et al.  Instability modes of cantilevered bars induced by fluid flow through attached pipes , 1967 .

[38]  C. D. Mote,et al.  Time Delay Instabilities in Large Order Systems With Controlled Follower Forces , 1972 .

[39]  C. Sundararajan,et al.  Influence of an elastic end support on the vibration and stability of Beck's column , 1976 .

[40]  Isaac Elishakoff,et al.  Does a Partial Elastic Foundation Increase the Flutter Velocity of a Pipe Conveying Fluid , 2001 .

[41]  M. Kh. Mullagulov.  Experimental-theoretical study of the stability of rods, compressed by follower forces , 1994 .

[42]  Yoshihiko Sugiyama,et al.  Experiment on flutter of cantilevered columns subjected to a rocket thrust , 1990 .

[43]  N. Alfutov,et al.  Stability of Elastic Structures , 2000 .

[44]  Tadakazu Katayama,et al.  STABILIZATION OF CANTILEVERED FLEXIBLE STRUCTURES BY MEANS OF AN INTERNAL FLOWING FLUID , 1996 .

[45]  G.T.S. Done,et al.  On the partial simulation of a nonconservative system by a conservative system , 1971 .

[46]  M. P. Païdoussis,et al.  A Physical Explanation of the Destabilizing Effect of Damping , 1998 .

[47]  A. N. Kounadis,et al.  Nonlinear Dynamic Buckling and Stability of Autonomous Dissipative Discrete Structural Systems , 1995 .

[48]  Anthony N. Kounadis,et al.  On the paradox of the destabilizing effect of damping in non-conservative systems , 1992 .

[49]  H. Ziegler.  Trace Effects in Stability , 1971 .

[50]  N. Willems.  Experimental Verification of the Dynamic Stability of a Tangentially Loaded Cantilever Column , 1966 .

[51]  George Herrmann,et al.  Dynamic Behavior of Continuous Cantilevered Pipes Conveying Fluid Near Critical Velocities , 1981 .

[52]  Kunihide Sasou,et al.  Team errors: definition and taxonomy , 1999 .

[53]  G. Herrmann,et al.  Determinism and Uncertainty in Stability , 1971 .

[54]  Stephen H. Crandall,et al.  The effect of damping on the stability of gyroscopic pendulums , 1995 .

[55]  L. Taylor,et al.  The Neglect of Experiment , 1986 .

[56]  M. Bernhard.  Introduction to Chaotic Dynamical Systems , 1992 .

[57]  Graham Priest,et al.  Can Theories Be Refuted , 1976 .

[58]  D. S. Dermendjian-Ivanova.  Critical flow velocities of a simply supported pipeline on an elastic foundation , 1992 .

[59]  Horace Lamb.  On kinetic stability , 1908 .

[60]  Isaac Elishakoff,et al.  On a new “destabilization” phenomenon: effect of rotary damping , 1987 .

[61]  I. F. A. Wahed,et al.  The Instability of a Cantilever on an Elastic Foundation under the Influence of a Follower Force , 1975 .

[62]  Daniel J. Inman,et al.  Matching Analytical Models with Experimental Modal Data in Mechanical Systems , 1990 .

[63]  Michael P. Païdoussis,et al.  Pipes Conveying Fluid: A Model Dynamical Problem , 1993 .

[64]  Peter A. Djondjorov.  DYNAMIC STABILITY OF PIPES PARTLY RESTING ON WINKLER FOUNDATION , 2001 .

[65]  G. M. L. Gladwell.  Follower forces : Leipholz's early researches in elastic stability , 1990 .

[66]  Z. Bažant,et al.  Stability Of Structures , 1991 .

[67]  John Horgan,et al.  From Complexity to Perplexity , 1995 .

[68]  G. L. Anderson,et al.  The influence of rotatory inertia, tip mass, and damping on the stability of a cantilever beam on an elastic foundation , 1975 .

[69]  J. A. Walker,et al.  Mathematical modeling of discrete nonconservative dynamic systems , 1972 .

[70]  Maher N. Bismarck-Nasr,et al.  Dynamic stability of shallow shells subjected to follower forces , 1995 .

[71]  R. A. Stein,et al.  Vibration of Pipes Containing Flowing Fluids , 1970 .

[72]  K. H. Lee,et al.  A predictor-corrector zig-zag model for the bending of laminated composite plates , 1996 .

[73]  Raymond H. Plaut.  Postbuckling Analysis of Nonconservative Elastic Systems , 1976 .

[74]  V. V. Bolotin.  Dynamic Stability of Structures , 1995 .

[75]  George Herrmann,et al.  Stability of a cantilevered bar subjected to a transverse follower force of fluid jet , 1970 .

[76]  G. Herrmann,et al.  The usefulness of adjoint systems in solving nonconservative stability problems of elastic continua. , 1969 .

[77]  G. Venkateswara Rao,et al.  Stability of tapered cantilever columns with an elastic foundation subjected to a concentrated follower force at the free end , 1982 .

[78]  Isaac Elishakoff,et al.  Remarks on the Static and Dynamic Imperfection-Sensitivity of Nonsymmetric Structures , 1980 .

[79]  K. Popp,et al.  Examples of Non-Smooth Mechanical Systems — An Overview — , 1999 .

[80]  J. J. Wu.  On missile stability , 1976 .

[81]  Anthony N. Kounadis,et al.  On the failure of static stability analyses of nonconservative systems in regions of divergence instability , 1994 .

[82]  Thomas Brooke Benjamin,et al.  Dynamics of a system of articulated pipes conveying fluid - I.Theory , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[83]  Hiromi Sugiyama,et al.  Numerical simulation by cubic-polynomial interpolation for unsteady, incompressible, viscous flow , 1995 .

[84]  W. T. Koiter.  UNREALISTIC FOLLOWER FORCES , 1996 .

[85]  M. Resnik,et al.  Aspects of Scientific Explanation. , 1966 .

[86]  Isaac Elishakoff,et al.  Generalization of smith-herrmann problem with the aid of computerized symbolic algebra , 1987 .

[87]  B. Tabarrok,et al.  A Note On The Dynamic Behavior Of Discretized Non-conservative Systems , 1993 .

[88]  Isaac Elishakoff,et al.  EFFECT OF ELASTIC FOUNDATIONS ON DIVERGENCE AND FLUTTER OF AN ARTICULATED PIPE CONVEYING FLUID , 2000 .

[89]  Anthony N. Kounadis,et al.  Qualitative criteria for dynamic buckling of imperfection sensitive nonconservative systems , 1998 .

[90]  D. C. Drucker,et al.  ON THE ROLE OF EXPERIMENT IN THE DEVELOPMENT OF THEORY , 1962 .

[91]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[92]  A. P. Seiranyan,et al.  Collision of eigenvalues in linear oscillatory systems , 1994 .

[93]  M. P. Paidoussis,et al.  Unstable oscillation of tubular cantilevers conveying fluid II. Experiments , 1966, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[94]  Max Beck,et al.  Die Knicklast des einseitig eingespannten, tangential gedrückten Stabes , 1952 .

[95]  Aron Zaslavsky.  Discussion on destabilizing effect of additional restraint on elastic bar structures , 1981 .

[96]  Y. Sugiyama,et al.  Dynamic stability of cantilevered timoshenko columns subjected to a rocket thrust , 1994 .

[97]  Michael P. Païdoussis,et al.  1992 CALVIN RICE LECTURE: Some Curiosity-Driven Research in Fluid Structure Interactions and Its Current Applications , 1993 .

[98]  B. Tabarrok,et al.  A dynamic method for measuring the critical load of a non-conservative composite column , 1990 .

[99]  Yoshihiko Sugiyama,et al.  Realistic Follower Forces , 1999 .

[100]  M. P. Païdoussis,et al.  Articulated Models of Cantilevers Conveying Fluid: The Study of a Paradox: , 1970 .

[101]  Jon Juel Thomsen,et al.  Vibrations and Stability , 2003 .

[102]  Sia Nemat-Nasser,et al.  Instability of an articulated cantilever induced by an impinging airjet , 1985 .

[103]  Vassil M. Vassilev,et al.  DYNAMIC STABILITY OF FLUID CONVEYING CANTILEVERED PIPES ON ELASTIC FOUNDATIONS , 2001 .

[104]  G L Anderson.  Qualitative Stability Characteristics of a Flexible Missile Subjected to a Circulatory Thrust. , 1977 .

[105]  R. Parnes,et al.  A paradoxical case in a stability analysis , 1977 .

[106]  Anthony N. Kounadis,et al.  On the reliability of classical divergence instability analyses of Ziegler's nonconservative model , 1992 .

[107]  W. Hauler,et al.  Influence of an elastic foundation on the stability of a tangentially loaded column , 1976 .

[108]  Julian J. Wu.  Missile Stability Using Finite Elements—an Unconstrained Variational Approach , 1976 .

[109]  G. L. Anderson.  The influence of a wieghardt type elastic foundation on the stability of some beams subjected to distributed tangential forces , 1976 .

[110]  F. Blottner,et al.  Accurate Navier-Stokes results for the hypersonic flow over a spherical nosetip , 1989 .

[111]  D. C. Drucker,et al.  Thoughts on the present and future interrelation of theoretical and experimental mechanics , 1968 .

[112]  B. Tabarrok,et al.  On a centripetally loaded model simulating Beck's column , 1989 .

[113]  Anthony N. Kounadis,et al.  Non-potential dissipative systems exhibiting periodic attractors in regions of divergence , 1997 .

[114]  P. M. Saunders,et al.  The kinetic stability of a tangentially loaded strut , 1969, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[115]  C. Sundararajan,et al.  Stability of columns on elastic foundations subjected to conservative and non-conservative forces , 1974 .

[116]  G. Anderson,et al.  On the role of the adjoint problem in dissipative, nonconservative problems of elastic stability , 1972 .

[117]  Yoshihiko Sugiyama,et al.  Stability of a Jointed FREE FREE Beam Under End Rocket Thrust , 1997 .

[118]  Michael P. Païdoussis,et al.  Dynamics of Tubular Cantilevers Conveying Fluid , 1970 .

[119]  N Oreskes,et al.  Verification, Validation, and Confirmation of Numerical Models in the Earth Sciences , 1994, Science.

[120]  Horst Leipholz,et al.  Die Knicklast des einseitig eingespannten Stabes mit gleichmässig verteilter, tangentialer Längsbelastung , 1962 .

[121]  George Herrmann,et al.  Instabilities of a Spatial System of Articulated Pipes Conveying Fluid , 1974 .

[122]  Earl H. Dowell,et al.  The suppression of a dynamic instability of an elastic body using feedback control , 1974 .

[123]  Sia Nemat-Nasser,et al.  Instability of a Mechanical System Induced by an Impinging Fluid Jet , 1969 .

[124]  W. T. Koiter.  Buckling of a flexible shaft under torque loads transmitted by Cardan joints , 1980 .

[125]  T. Beal.  Dynamic stability of a flexible missile under constant and pulsating thrusts , 1965 .

[126]  H. H. E. Leipholz.  On the occurrence of non-selfadjointness in the control of elastic structures , 1988 .

[127]  A. Pflüger.  Zur Stabilität des tangential gedrückten Stabes , 1955 .

[128]  T. E. Smith.  Buckling of a beam on a Wieghardt-type elastic foundation , 1969 .

[129]  Sia Nemat-Nasser,et al.  Torsional Instability of Cantilevered Bars Subjected to Nonconservative Loading , 1966 .

[130]  S. Majid Hassanizadeh,et al.  Model definition and model validation , 1994 .

[131]  M. A. De Rosa,et al.  Dynamic stability analysis of beams on two-parameter elastic soil subjected to partially tangential forces , 2003 .

[132]  Finn Jensen.  Editorial: How to succeed in modelling , 1999 .

[133]  C. Sundararajan,et al.  The Vibration and Stability of Elastic Systems Subjected to Follower Forces , 1975 .

[134]  George Herrmann,et al.  Flutter of Articulated Pipes at Finite Amplitude , 1975 .

[135]  John E. Mottershead,et al.  Parametric resonances in an annular disc, with a rotating system of distributed mass and elasticity; and the effects of friction and damping , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[136]  T. Faber,et al.  Fluid Dynamics for Physicists: Frontmatter , 1995 .

[137]  Vladimir V. Bolotin.  Dynamic Instabilities in Mechanics of Structures , 1999 .

[138]  H. Ziegler,et al.  Die Stabilitätskriterien der Elastomechanik , 1952 .

[139]  C. D. Mote,et al.  The maximum controlled follower force on a free-free beam carrying a concentrated mass , 1985 .

[140]  Isaac Elishakoff,et al.  Influence of various types of elastic foundation on the divergence and flutter of Ziegler's model structure , 1987 .

[141]  Thomas Brooke Benjamin,et al.  Dynamics of a system of articulated pipes conveying fluid - II. Experiments , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[142]  K. Huseyin.  Vibrations and stability of mechanical systems. III , 1976 .

[143]  Menahem Baruch,et al.  Note on static and dynamic instability of a non-uniform beam , 1977 .

[144]  S. C. Sinha,et al.  Influence of a viscoelastic foundation on the stability of Beck's column: An exact analysis , 1983 .

[145]  Yoshihiko Sugiyama,et al.  On an unduly simplified model in the non-conservative problems of elastic stability , 1976 .

[146]  Heow Pueh Lee,et al.  Dynamic stability of a tapered cantilever beam on an elastic foundation subjected to a follower force , 1996 .

[147]  G. Venkateswara Rao,et al.  Stability of short Beck and Leipholz columns on elastic foundation , 1983 .

[148]  A. Kornecki,et al.  On the Character of Instability of Certain Aeroelastic Systems , 1973 .

[149]  Olivier Doaré,et al.  LOCAL AND GLOBAL INSTABILITY OF FLUID-CONVEYING PIPES ON ELASTIC FOUNDATIONS , 2002 .

[150]  J. M. T. Thompson,et al.  ‘Paradoxical’ mechanics under fluid flow , 1982 .

[151]  A. Kornecki,et al.  The effect of an elastic foundation and of dissipative forces on the stability of fluid-conveying pipes , 1986 .

[152]  W. Hauger,et al.  Influence of internal and external damping on the stability of Beck's column on an elastic foundation , 1977 .

[153]  Giuliano Augusti,et al.  Instability of struts subject to radiant heat , 1968 .

[154]  Yoshihiko Sugiyama,et al.  Effect of concentrated mass on stability of cantilevers under rocket thrust , 1995 .

[155]  H. H. E. Leipholz.  Die direkte Methode der Variationsrechnung und Eigenwertprobleme der Technik , 1975 .

[156]  W. Roth,et al.  Instabilität durchströmter Rohre , 1964 .

[157]  John D. Bredehoeft,et al.  Ground-water models cannot be validated , 1992 .

[158]  Yoshihiko Sugiyama,et al.  Flutter of Cantilevered Column Under Rocket Thrust , 1995 .

[159]  Ya.G. Panovko,et al.  The paradoxal influence of an increase of rigidity on buckling loads and natural frequencies for elastic systems , 1993 .

[160]  Knickung gerader Stäbe durch Druck und konservative Torsion , 1955 .

[161]  Yoshihiko Sugiyama,et al.  EXPERIMENTAL VERIFICATION OF DYNAMIC STABILITY OF VERTICAL CANTILEVERED COLUMNS SUBJECTED TO A SUB-TANGENTIAL FORCE , 2000 .

[162]  Giovanni Menditto.  Elastic stability of a uniform cantilevered beam on elastic foundation with a shear layer subjected to a follower force , 1974 .

[163]  Yoshihiko Sugiyama,et al.  Dynamic stability of columns subjected to follower loads : A survey , 2000 .

[164]  George Herrmann,et al.  Stability of a beam on an elastic foundation subjected to a follower force. , 1972 .

[165]  Toshihiro Noda,et al.  Studies on Stability of Two-degree-of-freedom Articulated Pipes Conveying Fluid : Effect of an Attached Mass and Damping , 1981 .

[166]  A. N. Kounadis.  Stability of Elastically Restrained Timoshenko Cantilevers With Attached Masses Subjected to a Follower Force , 1977 .

[167]  I. Elishakoff,et al.  Discrete-continuous elastic foundation may leave the flutter load of the Pflüger column unaffected , 1986 .

[168]  David C. Zimmerman,et al.  Model validation and verification of large and complex space structures , 2000 .

[169]  Roman Bogacz,et al.  On the shape of characteristic curves for optimal structures under non-conservative loads , 1981 .

[170]  Olivier Doaré,et al.  Effect of Length on the Instability of Hanging Pipes , 2002 .