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Calculation of the eigenfrequencies for an infinite circular cylinder

무한 원통형 실린더의 고유진동수에 관한 연구

Baik, Kyungmin;Ryue, Jung-Soo;Shin, Ku-Kyun
백경민;유정수;신구균

  • Received : 2015.07.31
  • Accepted : 2015.10.02
  • Published : 2016.01.31

Abstract

Present study shows three different methods finding the eigenfrequencies of an infinite circular cylinder under free-vibration; Elasticity theory that can be applied to general case, thin-shell theory that can be effectively applied to the cylinders with small thickness, and numerical study using Finite Element Method (FEM). The results obtained from those methods were verified through the cross check among the calculations. Changing the thickness of the cylinder for a fixed outer radius, all the eigenfrequencies below 1 kHz were found and their dependences on the modal index and the thickness were observed.

Keywords

Cylinder;Eigenfrequency;Elasticity;Thin-shell;FEM

References

  1. H. K. Jo, "A study of comparison with free wave number between a new cylinderical wave equation and the wave equation by Junger and Feit" (in Korean), J. Acoust. Soc. kr. 15, 47-51 (1996).
  2. L. Pochhammer, "Uber die fortpflanzungs -geschwindigkeiten kleiner Schwingungen in unbegrenzten isotropen Kreiszylinder (On the propagation velocities of small vibrations in an infinite isotropic cylinder)" (in German), Zeitschrift fur Reine und Angewandte Mathematik 81, 324-336 (1876).
  3. C. Chree, "The equation of an isotropic elastic solid in polar and cylindrical coordinates, their solution and applications," Transactions of the Cambridge Philosophical Society 14, 250-369 (1889).
  4. J. A. McFadden, "Radial vibrations of thick-walled hollow cylinders," J. Acoust. Soc. Am. 26, 714-715 (1954). https://doi.org/10.1121/1.1907405
  5. J. Ghosh, "Longitudinal vibrations of a hollow cylinder," Bull. Calcutta Math. Soc. 14, 31-40 (1923).
  6. D. C. Gazis, "Three-dimensional investigation of the propagation of waves in hollow circular cylinders. I. Analytical foundation," J. Acoust. Soc. Am. 31, 568-573 (1959). https://doi.org/10.1121/1.1907753
  7. Leissa, Vibration of shells, (NASASP-288, National Aeronautics and Space Administration, 1973).
  8. A. L. Fetter and J. D. Walecka, Theoretical Mechanics of Particles and Continua (Dover, New York, 2003), pp. 471-473.
  9. E. A. Skelton and J. H. James, Theoretical acoustics of underwater structures, (Imperial College Press, London, 1997), pp. 241-244.
  10. COMSOL, COSMOL Multiphysics Reference Manual, v4.3b., 2013.

Acknowledgement

Supported by : 국방과학연구소