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Axially symmetric elastic waves in a laminated compressible composite material with initial stresses

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Conclusions

From an analysis of the above results for ζ=1 we can conclude the following:

  1. 1.

    The initial stresses have a substantial effect on the phase velocities of the generated waves.

  2. 2.

    There are frequencies at which the relative phase velocity is independent of the initial stresses.

  3. 3.

    Each mode has a frequency range in which the variation of the phase velocity caused by the initial stresses is strongly dependent on the frequency.

  4. 4.

    As the ratio of layer thicknesses varies, there is also a variation both in the critical frequencies and in the nature of the dependence of the phase velocity on the frequency and on the initial stresses.

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Literature Cited

  1. 1.

    L. M. Brekhovskikh, Waves in Laminated Media [in Russian], Izd. Akad. Nauk SSSR, Moscow (1957).

  2. 2.

    A. N. Guz', Stability of Elastic Bodies under Finite Deformations [in Russian], Naukova Dumka, Kiev (1973).

  3. 3.

    A. N. Guz', “On the theory of composite materials with initial stresses,” in: Mechanics of Deformed Bodies and Structures [in Russian], Nauka, Moscow (1975), pp. 140–148.

  4. 4.

    A. N. Guz', “Linearized theory of the propagation of elastic waves in bodies with initial stresses,” Prikl. Mekh.,14, No. 4, 3–32 (1978).

  5. 5.

    A. N. Guz', A. P. Zhuk, and F. G. Makhort, Waves in a Layer with Initial Stresses [in Russian], Naukova Dumka, Kiev (1976).

  6. 6.

    A. N. Guz' and Le Minh Khanh, “Wave propagation in composite laminated materials with large initial deformations,” Prikl. Mekh.,12, No. 1, 3–11 (1976).

  7. 7.

    A. N. Guz', F. G. Makhort, and O. I. Gushcha, Introduction to Acousticoelasticity [in Russian], Naukova Dumka, Kiev (1977).

  8. 8.

    A. N. Guz', F. G. Makhort, O. I. Gushcha, and V. K. Lebedev, “On the theory of wave propagation in an elastic isotropic body with initial deformations,” Prikl. Mekh.,6, No. 12, 42–49 (1970).

  9. 9.

    Le Minh Khanh, “Wave propagation along layers in laminated compressible materials with initial deformations,” Prikl. Mekh.,13, No. 9, 21–26 (1977).

  10. 10.

    S. M. Rytov, “Acoustic properties of finely laminated media,” Akust. Zh.,2, No. 1, 71–78 (1956).

  11. 11.

    San, Akhenbach, and German, “Harmonic waves in a laminated medium which are propagated in the direction of lamination,” Proc. ASME [Russian translation], Prikl. Mekh., No. 2, 86–88 (1968).

  12. 12.

    N. A. Shul'ga, Fundamentals of the Mechanics of Laminated Media with Periodic Structure [in Russian], Naukova Dumka, Kiev (1981).

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Additional information

Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Kiev Scientific-Research Institute for Microinstruments. Translated from Prikladnaya Mekhanika, Vol. 20, No. 7, pp. 3–10, July, 1984.

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Guz', A.N., Sitenok, N.A. & Zhuk, A.P. Axially symmetric elastic waves in a laminated compressible composite material with initial stresses. Soviet Applied Mechanics 20, 589–596 (1984). https://doi.org/10.1007/BF00891714

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Keywords

  • Layer Thickness
  • Composite Material
  • Phase Velocity
  • Relative Phase
  • Elastic Wave