Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The interaction of an acoustic wave and an elastic spherical shell


Author: P. Mann-Nachbar
Journal: Quart. Appl. Math. 15 (1957), 83-93
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/88898
MathSciNet review: 88898
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Abstract: The effect of the impact of a plane pressure wave on an elastic spherical shell is considered, taking into account both the incident and diffracted waves. An infinite series (mode) solution is used and numerical results are obtained for the case of a steel shell in water. It is shown that a simple quasi-static system can be used to find a very good approximation for the stress. The total acceleration on initial impact is found exactly and seen to differ markedly from the accelerations associated with the lower vibrational modes.


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

  • [1] G. F. Carrier, The interaction of an acoustic wave and an elastic cylindrical shell, Brown University report to the Office of Naval Research under Contract N7onr-35810, No. Bll-4, 1951
  • [2] R. D. Mindlin and H. H. Bleich, Response of an elastic cylindrical shell to a transverse, step shock wave, J. Appl. Mech. 20 (1953), 189–195. MR 0059166
  • [3] J. H. Jellet, On the properties of extensible surfaces, Roy. Irish Acad. Trans. 22, Part V (1855)
  • [4] S. Timoshenko, Theory of plates and shells, 1st Ed., McGraw-Hill, New York and London, 1940
  • [5] Horace Lamb, On the Vibrations of a Spherical Shell, Proc. London Math. Soc. S1-14, no. 1, 50. MR 1576271, https://doi.org/10.1112/plms/s1-14.1.50
  • [6] J. H. Huth and J. D. Cole, Elastic stress waves produced by pressure loads on a spherical shell, J. Appl. Mech. 22, No. 4, 473-478 (1955)

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DOI: https://doi.org/10.1090/qam/88898
Article copyright: © Copyright 1957 American Mathematical Society


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