Soviet Applied Mechanics

, Volume 15, Issue 6, pp 451–463 | Cite as

Analysis of the modes of vibration of a circular disk in the vicinity of thickness resonance

  • V. T. Grinchenko
  • V. V. Meleshko


Circular Disk Thickness Resonance 
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Literature Cited

  1. 1.
    V. A. Babeshko, “Conditions of radiation for an elastic layer,” Dokl. Akad. Nauk SSSR,213, No. 3, 547–549 (1973).Google Scholar
  2. 2.
    P. V. Burlii and I. Ya. Kucherov, “Inverse elastic waves in plates,” Pis'ma Zh. Eksp. Teor. Fiz.,26, No. 9, 644–647 (1977).Google Scholar
  3. 3.
    V. M. Byrdin, “Conditions of radiation for some boundary-value problems with the Helmholtz equation,,” Dokl. Akad. Nauk SSSR,238, No. 2, 293–294 (1978).Google Scholar
  4. 4.
    I. P. Golyamina, “On the question of vibrations in the thickness of polarized plates of barium titanate,” Akust. Zh.,1, No. 1, 40–47 (1955).Google Scholar
  5. 5.
    V. T. Grinchenko, “Properties of the dynamic deformation of extended cylinders and plates in the region of high frequencies,” Prikl. Mekh.,13, No. 10, 43–49 (1977).Google Scholar
  6. 6.
    V. T. Grinchenko, Equilibrium and Steady-State Vibrations in Elastic Bodies of Finite Dimensions [in Russian], Naukova Dumka, Kiev (1978).Google Scholar
  7. 7.
    V. T. Grinchenko, V. L. Karlash, V. V. Malyeshko, and A. F. Ulitko, “Investigation of plane vibrations of rectangular piezoceramic plates,” Prikl. Mekh.,12, No. 5, 71–78 (1967).Google Scholar
  8. 8.
    V. T. Grinchenko and V. V. Malyeshko, “High-frequency axisymmetric vibrations of circular disks,” Prikl Mekh.,12, No. 12, 60–68 (1967).Google Scholar
  9. 9.
    W. Cady, Piezoelectricity and its Practical Applications [Russian translation], IL, Moscow (1949).Google Scholar
  10. 10.
    V. V. Madorskii and Yu. A. Ustinov, “Construction of a system of homogeneous solutions and analysis of the roots of the dispersion equation of antisymmetric vibrations of a piezoelectric slab,” Prikl. Mekh. Tekh. Fiz., No. 6, 138–146 (1967).Google Scholar
  11. 11.
    T. Meeker and A. Meitzler, “Waveguide propagation in extended cylinders and plates,” in: Physical Acoustics, W. Mason (editor), Academic Press.Google Scholar
  12. 12.
    J. R. Pierce, Almost All About Waves, MIT Press (1964).Google Scholar
  13. 13.
    B. A. Auld, Acoustic Fields and Waves in Solids, Vol. II, Wiley-Interscience, New York (1973).Google Scholar
  14. 14.
    B. A. Auld and E. D. Tsao, “A variational analysis of edge resonance in a semiinfinite plate,” IEEE Trans. Sonics Ultrason.,SU-24, No. 5, 317–326 (1977).Google Scholar
  15. 15.
    D. C. Gazis and R. D. Mindlin, “Extensional vibrations and waves in a circular disk and a semiinfinite plate,” J. Appl. Mech.,27, No. 3, 541–547 (1960).Google Scholar
  16. 16.
    R. Holland, and E. P. EerNisse, “Design of piezoelectric devices,” MIT Press, Cambridge (1969).Google Scholar
  17. 17.
    S. Ikegami, “Calculated frequency spectra of axisymmetric extensional vibrations in disks with Poisson's ratio of 1/3,” J. Acoust. Soc. Am.,64, No. 1, pp. 325–327 (1978).Google Scholar
  18. 18.
    S. Ikegami, T. Nagata, and Y. Nakajima “Frequency spectra of extensional vibration in Pb(ZrTi)O3 disks with Poisson's ratio larger than 1/3,” J. Acoust. Soc. Am.,60, No. 1, 113–116 (1976).Google Scholar
  19. 19.
    S. Ikegami, I. Ueda, and S. Kobayashi, “Frequency spectra of resonant vibration in disk plates of PbTiO3 piezoelectric ceramics,” J. Acoust. Soc. Am.,55, No. 2, 329–344 (1974).Google Scholar
  20. 20.
    Y. Kagawa and T. Yamabushi, “Finite element approach for a piezoelectric circular rod,” IEEE Trans. Sonics Ultrason.,SU-23, No. 6, 379–385 (1976).Google Scholar
  21. 21.
    A. H. Meitzler, “Backward-wave transmission of stress pulses in elastic cylinders and plates,” J. Acoust. Soc. Am.,38, No. 5, 835–842 (1965).Google Scholar
  22. 22.
    M. Onoe, “The contour vibrations of thin rectangular plates,” J. Acoust. Soc. Am.30, No. 11, 1159–1164 (1958).Google Scholar
  23. 23.
    G. H. Schmidt, “Resonances of an unbounded piezoelectric plate with circular electrodes,” Int. J. Eng. Sci.,15, No. 8, 495–510 (1977).Google Scholar
  24. 24.
    G. Schmidt, R. Grohmann, and V. Lössner, “Dickenschwingungen Kreisförmiger Scheiben aus Bariumtitanatkeramik,” Acustica,13, No. 3, 131–139 (1963).Google Scholar
  25. 25.
    G. Schmidt, and L. Kutschabsky, “Schwingungsformen zylindrischer Scheiben aus Bariumtitanatkeramik,” Acustica,10, No. 1, 30–34 (1960).Google Scholar
  26. 26.
    P. Schabel, “Dispersion of thickness bibrations of piezoceramic disk resonators,” IEEE Trans. Sonics Ultrason.,SU-25, No. 1, 16–24 (1978).Google Scholar
  27. 27.
    E. A. G. Shaw, “On the resonant vibrations of thick barium titanate disks,” J. Acoust. Soc. Am.,28, No. 1, 38–50 (1956).Google Scholar
  28. 28.
    W. Soedel and M. Dhar “Difficulties in finding modes experimentally when several contribute to a resonance,” J. Sound. Vibr.,58, No. 1, 27–38 (1978).Google Scholar
  29. 29.
    P. J. Torvic, “Reflection of wave trains in semiinfinite plates,” J. Acoust. Soc. Am.,41, No. 2, 346–353 (1967).Google Scholar
  30. 30.
    J. Zemanek, “An experimental and theoretical investigation of elastic wave propagation in a cylinder,” J. Acoust. Soc. Am.,51, No 1, 265–283 (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1979

Authors and Affiliations

  • V. T. Grinchenko
  • V. V. Meleshko

There are no affiliations available

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