Structural Engineering and Mechanics

  • 제4권3호
  • /
  • Pages.209-226
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  • 1996
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

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A spectrally formulated finite element method for vibration of a tubular structure

  • Horr, A.M. (Department of Civil & Mining Engineering, University of Wollongong) ;
  • Schmidt, L.C. (Department of Civil & Mining Engineering, University of Wollongong)
  • 발행 : 1996.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

One of the major divisions in the mathematical modelling of a tubular structure is to include the effect of the transverse shear stress and rotary inertia in vibration of members. During the past three decades, problems of vibration of tubular structures have been considered by some authors, and special attention has been devoted to the Timoshenko theory. There have been considerable efforts, also, to apply the method of spectral analysis to vibration of a structure with rectangular section beams. The purpose of this paper is to compare the results of the spectrally formulated finite element analyses for the Timoshenko theory with those derived from the conventional finite element method for a tubular structure. The spectrally formulated finite element starts at the same starting point as the conventional finite element formulation. However, it works in the frequency domain. Using a computer program, the proposed formulation has been extended to derive the dynamic response of a tubular structure under an impact load.

키워드

참고문헌

  1. Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, New Jersey: Prentice-Hall.
  2. Cowper, G. R. (1996), "The shear coefficient in Timoshenkos beam theory", J. of Applied Mechanics, 335-340.
  3. Doyle, J. F. and Farris, T. N. (1990), "A spectrally formulated finite element for flexural wave propagation in beams", Int. J. of Analytical And Experimental Modal Analysis, 99-107.
  4. Gopalarkishnan, S., Martin, M. and Doyle, J. E. (1992), "A matrix methodology for spectral analysis of wave propagation in multiple connected Timoshenko beams", J. of Sound and Vibration, 11-24.
  5. Horr, A. M. and Schmidt, L. C. (1995), "Closed-form solution for the Timoshenko beam theory using a computer-based mathematical package", Int. J. of Computers & Structures, 55, 405-412. https://doi.org/10.1016/0045-7949(95)98867-P
  6. Hutchinson, J. R. (1986), "Vibration of free hollow circular cylinders", J. of Applied Mechanics, 53, 641-646. https://doi.org/10.1115/1.3171824
  7. Przemieniecki, J. S. (1968), Theory of Matrix Structrual Analysis, McGraw-Hill, New York.
  8. Timoshenko, S. P. (1921), "On the correction for shear of the differential equation for transverse vibrations of prismatic bars", Philosophical Magazine, 41, 744-746. https://doi.org/10.1080/14786442108636264

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