Summary
The stress and deformation states are investigated in a cylindrical elastic rod which has been moving with a constant initial velocityv o in its longitudinal direction before being suddenly elastically fixed at its trailing end. A stress amplifying factor is evaluated depending on the stiffness of the fixation and the rod showing that the maximum stress in the rod may be increased significantly by an elastic fixation in comparison to a rigid blocking of the trailing end.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Lorenz, H.: Technische Elastizitätslehre. München Berlin: Oldenburg 1913.
Cottrell, A. H.: The mechanical properties of matter. New York: J. Wiley 1964.
Love, A. E. H.: A treatise on the mathematical theory of elasticity, 4th ed., pp. 281–284. New York: Dover Publications 1944.
Pochhammer, L.: Über die Fortpflanzungsgeschwindigkeiten kleiner Schwingungen in einem unbegrenzten isotropen Kreiszylinder. J. Math. (Crelle)81, p. 324 (1876); cited in [3], p. 287.
Chree, C.: The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solution and application. Cambridge Phil. Soc. Trans.14 (1889); cited in [3], p. 278.
Bierwirth, S., Najar, J.: Dispersion der Wellenausbreitung in Stäben bei der Untersuchung der dynamischen Zugfestigkeit in Al2O3. In: 23. Vortragsveranstaltung des DVM-Arbeitskreises Bruchvorgänge, pp. 423–432. Berlin: DVM-Verlag 1991.
Kenedy, L. W., Jones, O. E.: Longitudinal wave propagation in a circular bar loaded suddenly by a radially distributed end stress. J. Appl. Mech.36, 470–478 (1969).
Alterman, Z., Karal, F. C., Jr.: Propagation of elastic waves in a semi-infinite cylindrical rod using finite difference methods. J. Sound Vibr.13, 115–145 (1970).
Singh, M. C., Frydrychowicz, W.: Wave propagation in nonhomogeneous thin elastic rods subject to time dependent stress impact. J. Sound Vibr.79, 341–350 (1981).
Doetsch, G.: Anleitung zum praktischen Gebrauch der Laplace-Transformation und der Z-Transformation, 4th ed., p. 1. München Wien:R. Oldenburg 1981.
Spiegel, M. R.: Laplace Transformationen, pp. 201. New York Düsseldorf: McGraw-Hill 1977.
Poularikas, A. D., Seely, S.: Signals and systems, pp. 290. Boston: PWS-KENT 1985.
Carslaw, H. S., Jaeger, J. C.: The conduction of heat in solids, 2nd ed., p. 492. Oxford: University Press 1959.
Abramowitz, M., Stegun, I. A.: Handbook of mathematical functions with formulas, graphs and mathematical tables, p. 225. New York: Dover Publications 1970.
Wolfram, S.: Mathematica: A system for doing mathematics by computer, 2nd ed. Redwood City: Addison-Wesley 1991.
Papoulis, A.: A new method of inversion of the Laplace transform. Q. Appl. Math.14, 405–414 (1957).
Stehfest, H.: Numerical inversion of Laplace transforms. CACM13, 47–49 624 (1970).
Talbot, A.: The accurate numerical inversion of Laplace transforms. J. Inst. Math. Appl.23, 97–120 (1979).
Wang, C. H., Jan, Y. S.: A neuristic approach to the inverse Laplace transform of higher order systems. Comput. Elect. Eng.5, 257–269 (1978).
Inoue, H., Kamibayashi, M., Kishimoto, K., Shibuya, T., Koizumi, T.: Numerical Laplace transformation and inversion using fast Fourier transform. JSME Int. J.35, 319–324 (1992).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Werner, E.A., Fischer, F.D. The stress state in a moving rod suddenly elastically fixed at its trailing end. Acta Mechanica 111, 171–179 (1995). https://doi.org/10.1007/BF01376928
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01376928