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UNREALISTIC FOLLOWER FORCES
Journal of Sound and Vibration (1996) 194(4), 636–638
UNREALISTIC FOLLOWER FORCES W. T. K Laboratory for Engineering Mechanics, P.O. Box 5033, 2600 GA Delft, The Netherlands (Received 6 July 1995)
It has been brought to my attention that, as Editor-in-Chief, acting on the advice of one of your referees, Professor Isaac Elishakoff, you have recently decided not to accept for publication a paper on the effect of follower forces. This is most welcome and hopefully effective. I am writing this letter in order to express my support of your decision and to explain my reasons for the proposed elimination of the abstraction of follower forces as external loads from the physical and engineering literature on elastic stability. The theory of elastic stability deals with the stability of equilibrium of elastic structures under the action of static external loads. In most problems of buckling the individual loads are of the type of gravity, invariant upon deflections of the structure, both in magnitude and direction. Such dead loads are conservative and the potential energy of each individual loading force is minus the scalar product of the force and the displacement vector of its point of application. Another example of static external loads is a uniform constant external pressure on the outer surface of a closed vessel, with a potential energy equal to the product of the pressure and the volume enclosed by the outer surface. The standard example of a follower force is a cantilever bar with a compressive load on the free end, which force always remains tangential to the elastic line. The abundant literature on such non-conservative follower forces in the second half of the present century is devoid of any mechanism by means of which experiments on follower forces can be performed. The absence of such physical evidence reduces the concept of follower forces to a ‘‘Gedankenexperiment’’ without consequences in the real world. An even more telling example of the absurdity of non-conservative static, purely configuration-dependent external loads, is a cantilever shaft loaded at its free end by a torque whose vector remains invariant, both in magnitude and direction, upon deflections of the shaft. Such a shaft would be dynamically unstable for any non-zero value of the torque. The moral of the arguement above is to authors and journal editors alike: beware of unrealistic follower forces.
EDITOR-IN-CHIEF’S REPLY P. E. D Institute of Sound and Vibration Research, University of Southampton, Highfield, Southampton SO17 1BJ, England (Received 17 November 1995)
Professor Koiter has warned us ‘‘authors and journal editors alike: beware of unrealistic follower forces’’, and indeed has ‘‘proposed elimination of the abstraction of follower forces as external loads from the physical and engineering literature on elastic stability’’. 636 0022–460X/96/290636 + 03 $18.00/0
7 1996 Academic Press Limited
637
He has also explained concisely in his Letter his reasons for this proposal. The basis of his reasoning is, I believe, contained in the following sentences from his Letter: ‘‘The standard example of following forces is a cantilever bar with a compressive load on the free end, which force always remains tangential to the elastic line. The abundant literature on such non-conservative follower forces is devoid of any mechanism by means of which experiments on follower forces can be performed. The absence of such physical evidence reduces the concept of follower forces to a ‘Gedankenexperiment’ without consequences in the real world’’. As an editor with some expertise in continuum mechanics, especially acoustics, very little in vibration, and practically zero in the elastic stability of structures, I can only wonder how it has come about that so many structural dynamicists over the past fifty years have adopted the follower force concept without its ever having been validated experimentally. In my ignorance, I had supposed that, for example, people modelling rockets as beams, and the thrust, due to the burning rocket fuel being expelled, as a follower force, had some experimental basis for believing in an at least approximate physical validity of such modelling. In the wider context, with which as an editor I am most concerned, this follower force concept is not the only example of inadequate, dubious or erroneous mathematical modelling of physical systems which has been accompanied by increasingly ‘‘abundant literature’’ during the past 50 years or so. Over a decade ago, a colleague asked me why JSV did not publish more papers on experimental structural dynamics. I could reply only with the question ‘‘Why are so few such papers submitted?’’. We all know that the principal answer to this question is ‘‘because it is so much easier and cheaper to do computer simulations nowadays than it is to perform real experiments’’. What we appear to have been increasingly forgetting is that mathematically generated data has scientific and engineering value only insofar as it corresponds to the data that the real experiments would have produced if we had done them. As JSV is a scientific/engineering journal the primary requirement of papers published in it is that they provide new scientific/engineering information. This information can be almost purely mathematical but only if it is shown to have physical meaning, or practical scientific/engineering applications. It is obligatory on authors providing such information that they demonstrate in their papers, by examples or otherwise, this physical relevance. To return to Professor Koiter’s proposal to eliminate the follower force concept from the scientific and engineering literature, I regret that I have to say that I do not believe that I have the right, as an editor, to reject ab initio all papers submitted in which follower force modelling is used. Rather, since the acquisition of scientific knowledge is an essentially collective process aimed at reaching mutual agreement among scientists about the validity of the concepts that they develop cooperatively, by testing experimentally and intellectually one another’s results and concepts, follower force modelling can be properly removed from our concepts only by mutual debate among all concerned—authors, journal editors, and perhaps especially referees. It would be improper for an editor to act as more than a chairman of this debate. Editors, however, will find out sooner than most how the debate is going: follower force modelling papers will no longer be recommended for publication by referees when a consensus against them has been reached. On the other hand, should someone come forward with an experimental validation of the follower force concept, to a reasonable approximation, for some specific physical system, then the day of universal rejection of follower force papers may never come. Speaking personally, I do not believe in the physical validity of the follower force concept, simply because I am not aware of any experimental demonstration of that validity. But I also recall that some 2000 years passed before the ancient Greek concept
638
of atoms was experimentally demonstrated. Editors, especially, must beware also of appointing themselves as judges of rectitude. I should think that the proper way to deal with this question of follower forces, and perhaps some other similar questions of the physical validity of mathematical models, would be for those concerned, both for and against, to organize a Conference, at which hopefully a consensus could be reached. Also I recall that some years ago the question of the second spectrum of Timoshenko beams was answered apparently conclusively by N. G. Stephen (1982 JSV 80(4), 578–582), as I have seen no mention of it since. In any case, until a consensus is reached, for my part as an editor I can rely only on referees’ opinions. I cannot unilaterally ban follower forces. Thus follower force papers which have been recommended for publication by referees may continue to appear in JSV from time to time: several such manuscripts are at present on the way to publication. Finally I must add that the Letters to the Editor section of JSV is always available to all who may wish to engage in the debate about follower forces, and any other matters relevant to sound and vibration.
UNREALISTIC FOLLOWER FORCES W. T. K Laboratory for Engineering Mechanics, P.O. Box 5033, 2600 GA Delft, The Netherlands (Received 6 July 1995)
It has been brought to my attention that, as Editor-in-Chief, acting on the advice of one of your referees, Professor Isaac Elishakoff, you have recently decided not to accept for publication a paper on the effect of follower forces. This is most welcome and hopefully effective. I am writing this letter in order to express my support of your decision and to explain my reasons for the proposed elimination of the abstraction of follower forces as external loads from the physical and engineering literature on elastic stability. The theory of elastic stability deals with the stability of equilibrium of elastic structures under the action of static external loads. In most problems of buckling the individual loads are of the type of gravity, invariant upon deflections of the structure, both in magnitude and direction. Such dead loads are conservative and the potential energy of each individual loading force is minus the scalar product of the force and the displacement vector of its point of application. Another example of static external loads is a uniform constant external pressure on the outer surface of a closed vessel, with a potential energy equal to the product of the pressure and the volume enclosed by the outer surface. The standard example of a follower force is a cantilever bar with a compressive load on the free end, which force always remains tangential to the elastic line. The abundant literature on such non-conservative follower forces in the second half of the present century is devoid of any mechanism by means of which experiments on follower forces can be performed. The absence of such physical evidence reduces the concept of follower forces to a ‘‘Gedankenexperiment’’ without consequences in the real world. An even more telling example of the absurdity of non-conservative static, purely configuration-dependent external loads, is a cantilever shaft loaded at its free end by a torque whose vector remains invariant, both in magnitude and direction, upon deflections of the shaft. Such a shaft would be dynamically unstable for any non-zero value of the torque. The moral of the arguement above is to authors and journal editors alike: beware of unrealistic follower forces.
EDITOR-IN-CHIEF’S REPLY P. E. D Institute of Sound and Vibration Research, University of Southampton, Highfield, Southampton SO17 1BJ, England (Received 17 November 1995)
Professor Koiter has warned us ‘‘authors and journal editors alike: beware of unrealistic follower forces’’, and indeed has ‘‘proposed elimination of the abstraction of follower forces as external loads from the physical and engineering literature on elastic stability’’. 636 0022–460X/96/290636 + 03 $18.00/0
7 1996 Academic Press Limited
637
He has also explained concisely in his Letter his reasons for this proposal. The basis of his reasoning is, I believe, contained in the following sentences from his Letter: ‘‘The standard example of following forces is a cantilever bar with a compressive load on the free end, which force always remains tangential to the elastic line. The abundant literature on such non-conservative follower forces is devoid of any mechanism by means of which experiments on follower forces can be performed. The absence of such physical evidence reduces the concept of follower forces to a ‘Gedankenexperiment’ without consequences in the real world’’. As an editor with some expertise in continuum mechanics, especially acoustics, very little in vibration, and practically zero in the elastic stability of structures, I can only wonder how it has come about that so many structural dynamicists over the past fifty years have adopted the follower force concept without its ever having been validated experimentally. In my ignorance, I had supposed that, for example, people modelling rockets as beams, and the thrust, due to the burning rocket fuel being expelled, as a follower force, had some experimental basis for believing in an at least approximate physical validity of such modelling. In the wider context, with which as an editor I am most concerned, this follower force concept is not the only example of inadequate, dubious or erroneous mathematical modelling of physical systems which has been accompanied by increasingly ‘‘abundant literature’’ during the past 50 years or so. Over a decade ago, a colleague asked me why JSV did not publish more papers on experimental structural dynamics. I could reply only with the question ‘‘Why are so few such papers submitted?’’. We all know that the principal answer to this question is ‘‘because it is so much easier and cheaper to do computer simulations nowadays than it is to perform real experiments’’. What we appear to have been increasingly forgetting is that mathematically generated data has scientific and engineering value only insofar as it corresponds to the data that the real experiments would have produced if we had done them. As JSV is a scientific/engineering journal the primary requirement of papers published in it is that they provide new scientific/engineering information. This information can be almost purely mathematical but only if it is shown to have physical meaning, or practical scientific/engineering applications. It is obligatory on authors providing such information that they demonstrate in their papers, by examples or otherwise, this physical relevance. To return to Professor Koiter’s proposal to eliminate the follower force concept from the scientific and engineering literature, I regret that I have to say that I do not believe that I have the right, as an editor, to reject ab initio all papers submitted in which follower force modelling is used. Rather, since the acquisition of scientific knowledge is an essentially collective process aimed at reaching mutual agreement among scientists about the validity of the concepts that they develop cooperatively, by testing experimentally and intellectually one another’s results and concepts, follower force modelling can be properly removed from our concepts only by mutual debate among all concerned—authors, journal editors, and perhaps especially referees. It would be improper for an editor to act as more than a chairman of this debate. Editors, however, will find out sooner than most how the debate is going: follower force modelling papers will no longer be recommended for publication by referees when a consensus against them has been reached. On the other hand, should someone come forward with an experimental validation of the follower force concept, to a reasonable approximation, for some specific physical system, then the day of universal rejection of follower force papers may never come. Speaking personally, I do not believe in the physical validity of the follower force concept, simply because I am not aware of any experimental demonstration of that validity. But I also recall that some 2000 years passed before the ancient Greek concept
638
of atoms was experimentally demonstrated. Editors, especially, must beware also of appointing themselves as judges of rectitude. I should think that the proper way to deal with this question of follower forces, and perhaps some other similar questions of the physical validity of mathematical models, would be for those concerned, both for and against, to organize a Conference, at which hopefully a consensus could be reached. Also I recall that some years ago the question of the second spectrum of Timoshenko beams was answered apparently conclusively by N. G. Stephen (1982 JSV 80(4), 578–582), as I have seen no mention of it since. In any case, until a consensus is reached, for my part as an editor I can rely only on referees’ opinions. I cannot unilaterally ban follower forces. Thus follower force papers which have been recommended for publication by referees may continue to appear in JSV from time to time: several such manuscripts are at present on the way to publication. Finally I must add that the Letters to the Editor section of JSV is always available to all who may wish to engage in the debate about follower forces, and any other matters relevant to sound and vibration.