The Journal of the Acoustical Society of Korea (한국음향학회지)

The Acoustical Society of Korea (한국음향학회)
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Calculation of the eigenfrequencies for an infinite circular cylinder

무한 원통형 실린더의 고유진동수에 관한 연구

  • 백경민 (한국표준과학연구원 유동음향센터) ;
  • 유정수 (울산대학교 조선해양공학부) ;
  • 신구균 (국방과학연구소 제6본부)
  • Received : 2015.07.31
  • Accepted : 2015.10.02
  • Published : 2016.01.31
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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.

본 논문은 무한 원통형 실린더의 자유진동에서 발생하는 고유진동수(eigenfrequency)를 구하는 3가지 방법에 대해 다루었다. 일반적인 경우에 적용될 수 있는 탄성 이론을 적용한 방법과 얇은 두께의 실린더에 효율적으로 적용될 수 있는 얇은 원통형 쉘 이론을 적용한 방법, 유한요소법(FEM: Finite Element Method)을 통한 수치 해석 방법을 통해 구해진 결과에 대한 비교 및 검증을 수행하였다. 주어진 실린더의 외반경에 두께를 서로 달리하여 1 kHz 이하에 존재하는 원통형 쉘의 고유진동수를 구하였고 모드수와 두께의 변화에 따른 이들 결과에 대해 관찰하였다.

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References

  1. 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).
  2. 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).
  3. 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
  4. J. Ghosh, "Longitudinal vibrations of a hollow cylinder," Bull. Calcutta Math. Soc. 14, 31-40 (1923).
  5. 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
  6. Leissa, Vibration of shells, (NASASP-288, National Aeronautics and Space Administration, 1973).
  7. A. L. Fetter and J. D. Walecka, Theoretical Mechanics of Particles and Continua (Dover, New York, 2003), pp. 471-473.
  8. E. A. Skelton and J. H. James, Theoretical acoustics of underwater structures, (Imperial College Press, London, 1997), pp. 241-244.
  9. COMSOL, COSMOL Multiphysics Reference Manual, v4.3b., 2013.
  10. 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).