Anelastic Waves in Thin Plates

  • Henryk Zorski
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

In investigating small displacements and the resulting state of stress in thin plates or shells obeying a linear stress-strain law, the three-dimensional problem is reduced to a two-dimensional one by means of a hypothesis concerning the distribution of the relevant geometric and mechanical quantities along the thickness of the shell or plate. The simplest hypothesis in bending is the Kirchhoff hypothesis, while for the motion “in the xy plane” it is usually assumed that a plane state of stress prevails. However, in the case of high frequencies and short wave lengths, particularly in the case of anelastic materials the equations of which contain higher time derivatives, the above assumptions are incorrect and it is necessary to establish a system of equations taking into account additional phenomena, such as rotary inertia, shear displacement, etc. This is done by changing the hypothesis or employing a method of successive approximations.

Keywords

Attenuation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Mikusinski, J.: Operational Calculus, London: Pergamon Press 1955.Google Scholar
  2. [2]
    Mindlin, R. D.: J. Appl. Mech. 73, 31–38 (1951).Google Scholar
  3. [3]
    Naghdi, P. M.: Proceedings of the Symposium on the Theory of Thin Elastic Shells, Amsterdam: North-Holland Publ. Co. 1960, p. 301.Google Scholar
  4. [4]
    Novozhilov, V. V., and P. M. Finkelsteyn: Prikladnaya Matematika i Mekhanika 7, 331 (1943).Google Scholar
  5. [5]
    Miklowitz, J.: Appl. Mech. Reviews 13, 865 (1960).MathSciNetGoogle Scholar
  6. [6]
    Kolsky, H.: Stress Waves in Solids, Oxford: Clarendon Press 1953.MATHGoogle Scholar
  7. [7]
    Zorski, H.: Warsaw: Biul. WAT 1957.Google Scholar
  8. [8]
    Herrmann, G., and I. Mirsky: J. Appl. Mech. 23, 563 (1956).MathSciNetMATHGoogle Scholar
  9. [9]
    Lurie, A. I.: Prikladnaya Mathematika i Mekhanika 4, 7 (1940).Google Scholar
  10. [10]
    Sneddon, I. N.: Fourier Transforms, New York/Toronto/London: McGraw-Hill 1951.Google Scholar

Copyright information

© Springer Verlag, Berlin / Göttingen / Heidelberg 1964

Authors and Affiliations

  • Henryk Zorski
    • 1
  1. 1.Polish Academy of SciencesWarsawPoland

Personalised recommendations