Applied Mathematics and Mechanics

, Volume 28, Issue 7, pp 861–872 | Cite as

Forced vibration and special effects of revolution shells in turning point range

  • Zhang Zhi-liang  (张志良)
  • Cheng Chang-jun  (程昌钧)Email author


The forced vibration in the turning point frequency range of a truncated revolution shell subject to a membrane drive or a bending drive at its small end or large end is studied by applying the uniformly valid solutions obtained in a previous paper. The vibration shows a strong coupling between the membrane and bending solutions: either the membrane drive or the bending drive causes motions of both the membrane type and bending type. Three interesting effects characteristic of the forced vibration emerge from the coupling nature: the non-bending effect, the inner-quiescent effect and the inner-membrane-motion-and-outer-bending-motion effect. These effects may have potential applications in engineering.

Key words

forced vibration special effect turning point range revolution shell 

Chinese Library Classification


2000 Mathematics Subject Classification

74K25 70J35 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Ross E W Jr. Transition solutions for axisymmetric shell vibrations[J]. Journal of Mathematical Physics, 1966, 54(4):335–355.Google Scholar
  2. [2]
    Gol’denveizer A L, Lidskiy V B, Tovstic P E. Free vibration of thin elastic shells[M]. Moscow: Nauka, 1979 (in Russian).Google Scholar
  3. [3]
    Zhang R J, Zhang W. Turning point solution for thin shell vibration[J]. International Journal of Solids and Structures, 1991, 27(10):1311–1326.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Zhang Z L, Cheng C J. Turning point solutions for axisymmetric shell vibrations[J]. Acta Mechanica Solida Sinica, 2006, 27(2):135–140 (in Chinese).Google Scholar
  5. [5]
    Zhang Z L, Cheng C J. Natural frequencies and mode shapes for axisymmetric vibrations of shells in turning point range[J]. International Journal of Solids and Structures, 2006, 43(18/19):5525–5540.CrossRefzbMATHGoogle Scholar
  6. [6]
    Hartung R F, Loden W A. Axismmetric vibration of conical shells[J]. Journal of Spacecraft and Rockets, 1970, 7(10):1153–1159.CrossRefGoogle Scholar
  7. [7]
    Zhang Z L, Cheng C J. Analytical solutions for axisymmetric vibration of loudspeaker cone in transitional range[J]. Available online 22 September, 2006. Http:// [20070507].Google Scholar
  8. [8]
    Kalnins A. Effect of bending on vibrations of spherical shells[J]. Journal of the Acoustical Society of America, 1964, 36(1):74–81.CrossRefMathSciNetGoogle Scholar
  9. [9]
    Frankort F J M. Vibration and sound radiation of loudspeaker cones[M]. Eindhoven: N. V. Philips’ Gloeilampenfabrieken, 1975.Google Scholar
  10. [10]
    Zhang Z L, Cheng C J. Vibrations of loudspeaker cones in transitional range[J]. Journal of the Audio Engineering Society, 2006, 54(7/8):598–603.Google Scholar

Copyright information

© Editorial Committee of Appl. Math. Mech. 2007

Authors and Affiliations

  • Zhang Zhi-liang  (张志良)
    • 1
    • 2
    • 3
  • Cheng Chang-jun  (程昌钧)
    • 1
    • 2
    Email author
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP. R. China
  2. 2.Department of MechanicsShanghai UniversityShanghaiP. R. China
  3. 3.Department of PhysicsZhejiang Normal UniversityJinhuaP. R. China

Personalised recommendations