Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Expanding axial wave on a submerged cylindrical shell


Authors: Tsun C. Fang and Jerome M. Klosner
Journal: Quart. Appl. Math. 28 (1970), 355-376
DOI: https://doi.org/10.1090/qam/99786
MathSciNet review: QAM99786
Full-text PDF Free Access

Abstract | References | Additional Information

Abstract: A double transform method is used to determine the response of a submerged, infinitely long, circular cylindrical shell to a plane acoustic wave which acts initially at an isolated cross section, and then proceeds to propagate along the axis of the cylinder, symmetrically with respect to that cross section.


References [Enhancements On Off] (What's this?)

  • [1] R. D. Mindlin and H. H. Bleich, Response of an elastic cylindrical shell to a transverse, step shock wave, J. Appl. Mech. 20, 189-195 (1953) MR 0059166
  • [2] M. L. Baron, The response of a cylindrical shell to a transverse shock wave, Proc. Second U.S. National Congress of Applied Mechanics, 1954, pp. 201-212
  • [3] J. H. Haywood, Response of an elastic cylindrical shell to a pressure pulse, Quart. J. Mech. Appl. Math. 11, 129-141 (1958) MR 0107416
  • [4] H. Herman and J. M. Klosner, Transient response of a periodically supported cylindrical shell immersed in a fluid medium, J. Appl. Mech. Ser. E 32, 562-568 (1965)
  • [5] J. W. Berglund and J. M. Klosner, Interaction of a ring-reinforced shell and a fluid medium, J. Appl. Mech. Ser. E 35, 139-147 (1968)
  • [6] G. F. Carrier, The response of a submerged cylindrical shell to an axially propagating acoustic wave, Contract N7 ONr-35810, no. B 11-19/7, Brown University, Providence, R.I., 1953
  • [7] F. Herrmann and J. E. Russell, Forced motions of shells and plates surrounded by an acoustic fluid, Proc. Sympos. Theory of Shells in Honor of Lloyd Hamilton Donnell, University of Houston, Houston, Texas, 1967, pp. 311-339
  • [8] A. Erdélyi, A symptotic expansions, Dover, New York, 1956
  • [9] G. F. Carrier, M. Krook and C. E. Pearson, Functions of a complex variable, McGraw-Hill, New York, 1966 MR 0222256
  • [10] H. Jeffreys and B. S. Jeffreys, Methods of mathematical physics, 2nd ed., Cambridge Univ. Press, London, 1950 MR 0035791
  • [11] M. V. Cerrillo, Elementary introduction to the theory of saddlepoint method of integration, Research Lab. Electronics, Techn. Report no. 55:2a (1950) M.I.T., Cambridge, Mass., 1954 MR 0065610
  • [12] T. C. Fang and J. M. Klosner, Expanding axial wave on a submerged cylindrical shell, Polytechnic Institute of Brooklyn, PIBAL Report no. 69-2, January 1969
  • [13] P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill, New York, 1961
  • [14] M. Abramowitz and I. A. Stegun (Editors), Handbook of mathematical functions, with formulas, graphs and mathematical tables, Nat. Bur. Standards Appl. Math. Series, 55, Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 1964; 3rd printing, with corrections, 1965 MR 0167642
  • [15] R. Folk, G. Fox, C.A. Shook and C. W. Curtis, Elastic strain produced by sudden application of pressure to one end of a cylindrical bar. I: Theory, J. Acoust. Soc. Amer. 30, 552-558 (1958) MR 0093189


Additional Information

DOI: https://doi.org/10.1090/qam/99786
Article copyright: © Copyright 1970 American Mathematical Society

American Mathematical Society