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The late-twentieth century resolution of a mid-nineteenth century dilemma generated by the eighteenth-century experiments of Ernst Chladni on the dynamics of rods

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References

  • 1784 Coulomb, Charles A. Recherches théoriques et expérimentales sur la force de torsion et sur l'élasticité des fils de métal. Histoire de l'Académie Royale des Sciences, Paris, pp. 229–269. [Reprinted in Mémoires de Coulomb, Vol. 1, Collections de Mémoires Relatifs à la Physique, publiés par la Société Française de Physique, Paris: Gauthier-Villars (1884), pp. 163–03.]

    Google Scholar 

  • 1787 Chladni, Ernst F. Entdeckungen über die Theorie des Klanges. Leipzig: Weidemanns Erben und Reich.

    Google Scholar 

  • 1794 Chladni, Ernst F. Ueber den Ursprung der von Pallas gefundenen Eisenmassen. (This paper on the Pallas iron is abstracted in The Philosophical Magazine, Tillock's series, II, 1, [1798].)

    Google Scholar 

  • 1798/1799 Chladni, Ernst F. Observations on a mass of iron ...; ... Some observations on fire-balls and shooting-stars; Observations on fireballs and hard bodies which have fallen from the atmosphere; The Philosophical Magazine, II, pp. 1–8, 225–231, 337–345.

    Google Scholar 

  • 1802 Chladni, Ernst F. Die Akustik. Leipzig.

  • 1809 Biot, Jean Baptiste. Expériences sur la propagation du son à travers les corps solides et à travers l'air, dans des tuyaux très-allongés. Mémoires de Physique et de Chimie de la Société d'Arcueil, 2, 405–423.

    Google Scholar 

  • 1816 Biot, Jean Baptiste. Dédication à M. Berthollet. Traité de Physique Expérimentale et Mathématique 1, i-xxiv, Paris.

    Google Scholar 

  • 1820 Savart, Félix. Mémoire sur la communication des mouvements entre les corps solides. Annales de Chimie et de Physique 14, 113–172.

    Google Scholar 

  • 1822 Chladni, Ernst F. Remarques concernant le Mémoire de M. Savart sur les communications des mouvements vibratoires entre les corps solides, imprimé dans les Annales de Chimie et de Physique, XIV, Juin, Annales de Chimie et de Physique, second series 20, 74–78.

    Google Scholar 

  • 1837 Savart, Félix. Recherches sur les vibrations longitudinales. Annales de Chimie et de Physique, second series 65, 337–402.

    Google Scholar 

  • 1851 Wertheim, Guillaume. Mémoire sur les vibrations des plaques circulaires. Annales de Chimie et de Physique, third series, 31, 5–19. [Presented to the French Academy, 1 October, 1849].

    Google Scholar 

  • 1851 Cauchy, Augustin L.; Regnault, Henri V.; and Duhamel, Jean M. Raport sur divers Mémoires de Wertheim. Comptes Rendus Acad. Sci. Paris 32, 326–330.

    Google Scholar 

  • 1861 Wertheim, Guillaume. On the cubical compressibility of certain solid homogeneous bodies. The Philosophical Magazine, fourth series 21, 447–451. (First published in the Comptes Rendus [1860] 51, 969–974: Mémoire sur la compressibilité cubique de quelques corps solides et homogènes.)

    Google Scholar 

  • 1861 Verdet, Marcel E. Notices sur les travaux scientifiques de M. Guillaume Wertheim, membre de la Société Philomathique de Paris, redigée sur la demande de la Société. L'Institut 29, Nos. 1432, 1433, 1434, Footnotes on pp. 198–201; 205–2091 and 213–216.

    Google Scholar 

  • 1867 Saint-Venant, Adhémard J. Mémoire sur le choc longitudinal de deux barres élastiques de grosseurs et de matières semblables ou différentes, et sur la proportion de leur force vive qui est perdue pour la translation ultérieure; et généralement sur le mouvement longitudinal d'un système de deux ou plusieurs prismes élastiques. J. Math. Pures Appl., second series 12, 237–376.

    Google Scholar 

  • 1886 Todhunter, Isaac, & Pearson, Karl. A History of the Theory of Elasticity and of the Strength of Materials, Vol. I. Cambridge: University Press (Vol. II, Parts I and II were first published in 1893.) Volumes I and II were reprinted in Dover Publications, New York (1960).

    Google Scholar 

  • 1893 Todhunter, Isaac, & Pearson, Karl. A History of the Theory of Elasticity and of the Strength of Materials, Vol. II, Parts I and II. Cambridge: University Press.

    Google Scholar 

  • 1899 Straubel, Constantin R. Ueber die Elasticitätszahlen und Elasticitätsmoduln des Glases. Annalen der Physik und Chemie, Neue Folge 68, 369–413.

    Google Scholar 

  • 1956 Bell, James F. Determination of dynamic plastic strain through the use of diffraction gratings. Jnl. of Applied Physics, 27, No. 10, 1109–1113.

    Google Scholar 

  • 1958 Bell, James F. Normal incidence in the determination of large strain through the use of diffraction gratings. Proceedings, Third U.S. National Congress of Applied Mechanics; Brown University, Providence, Rhode Island; 489–493.

    Google Scholar 

  • 1960a Bell, James F. Propagation of large amplitude waves in annealed aluminum. Jnl. of Applied Physics, 31, No. 2, 277–282.

    Google Scholar 

  • 1960b Bell, James F. Study of initial conditions in constant velocity impact. Jnl. of Applied Physics, 31, No. 12, 2188–2195.

    Google Scholar 

  • 1960c Bell, James F. Diffraction grating strain gauge. Proceedings, Society for Experimental Stress Analysis, 17, No. 2, 51–64.

    Google Scholar 

  • 1960d Bell, James F. The initial development of an elastic strain pulse propagating in a semi-infinite bar. U.S. Army Ballistics Research Laboratory, Technical Report No. 6, The Johns Hopkins University.

  • 1961a Bell, James F. Experimental study of the interrelation between the theory of dislocations in polycrystalline media and finite amplitude wave propagation in solids. Jnl. of Applied Physics, 32, No. 10, 1982–1993.

    Google Scholar 

  • 1961b Bell, James F. Further experimental study of the unloading phenomenon in constant velocity impact. Jnl. Mech. & Physics of Solids, 9, 261–278.

    Google Scholar 

  • 1961 Truesdell, Clifford A. General and exact theory of waves in finite elastic strain. Archive for Rational Mechanics and Analysis, 8, No. 3, 263–352. Corrected reprint in Continuum Mechanics, Part IV, Problems of Non-linear Elasticity; Internat'l. Science Review Series NY-London-Paris: Gordon & Breach 1965. Also in: Wave Propagation in Dissipative Materials. NY: Springer, 1965.

    Google Scholar 

  • 1962 Bell, James F. Experiments on large amplitude waves in finite elastic strain. Proceedings, International Union of Theoretical and Applied Mechanics, Symposium on Second-order Effects in Elasticity, Plasticity, and Fluid Dynamics; Haifa, Israel. [Pergamon Press: Oxford-Paris-New York; pp. 173–186 (1964).]

    Google Scholar 

  • 1963a Bell, James F. The initiation of finite amplitude waves in annealed metals. Proceedings, I.U.T.A.M. (International Union of Theoretical and Applied Mechanics): Stress Waves in Anelastic Solids; Symposium, Brown University, Providence, Rhode Island. [Springer-Verlag: Berlin-Göttingen-Heidelberg; pp. 166–182(1964).]

    Google Scholar 

  • 1963b Bell, James F. Single, temperature-dependent stress-strain law for the dynamic plastic deformation of annealed face-centred cubic metals. Jnl. of Applied Physics, 34, No. 1, 134–141.

    Google Scholar 

  • 1968 Bell, James F. The Physics of Large Deformation of Crystalline Solids. Springer Tracts in Natural Philosophy, Vol. 14. Springer-Verlag: Berlin-Heidelberg-New York. 253 pages.

    Google Scholar 

  • 1973 Bell, James F. The Experimental Foundations of Solid Mechanics, Handbuch der Physik, VIa/1. Springer-Verlag: Berlin-Heidelberg-NY 813 pages. Reprinted (1984) (Springer-Verlag) with title: Mechanics of Solids, Vol. 1: The Experimental Foundations of Solid Mechanics. Russian translation (two volumes) (1984): The Experimental Foundations of Solid Mechanics, from Handbuch der Physik, VIa/1. Moscow, U.S.S.R. (NAUKA).

    Google Scholar 

  • 1981 Acloque, Paul. Oscillations et Stabilité selon Foucault: Critique Historique et Expérimentale. (Collection des travaux de l'Académie Internationale d'Histoire des Sciences, 28, 149 pages. Paris: Éditions du Centre National de la Recherche Scientifique.

  • 1987a Bell, James F. The generation of transverse radial shear waves at a boundary between the domains of plasticity and elasticity. Internat'l Jnl. of Plasticity, 3, No. 2; 91–114.

    Article  Google Scholar 

  • 1987b Bell, James F. A confluence of experiment and theory for waves of finite strain in the solid continuum. Dynamical Problems in Continuum Physics; edited by J. L. Bona, C. Dafermos, J. L. Ericksen, & D. Kinderlehrer. Springer-Verlag; pp. 89–130.

  • 1988 Bell, James F. Plane stress, plane strain, and pure shear at large finite strain. Internat'l Jnl. of Plasticity, 4, 127–148.

    Article  Google Scholar 

  • 1989 Bell, James F. Experiments on the kinematics of large plastic strain in ordered solids. Internat'l Jnl. of Solids & Structures, 3, 267–278.

    Google Scholar 

  • 1990a Bell, James F. Material objectivity in an experimentally based incremental theory of large finite plastic strain. Internat'l Jnl. of Plasticity, 6, 293–314.

    Article  Google Scholar 

  • 1990b Bell, James F. The role of radial motion in the dynamic plasticity of rods. Internat'l Jnl. of Plasticity, 6, 665–676. (And see: Abstract, in Proceedings, Plasticity '89 Symposium, Mie University, Tsu, Japan [August, 1989]. Oxford: Pergamon Press; pp. 375–379.)

    Article  Google Scholar 

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  1. The Johns Hopkins University, Baltimore, Maryland

    James F. Bell

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Communicated by C. Truesdell

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Bell, J.F. The late-twentieth century resolution of a mid-nineteenth century dilemma generated by the eighteenth-century experiments of Ernst Chladni on the dynamics of rods. Arch. Hist. Exact Sci. 43, 251–273 (1991). https://doi.org/10.1007/BF00389434

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