Structural Engineering and Mechanics

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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)
  • Published : 1996.05.25
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Abstract

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.

Keywords

References

  1. Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, New Jersey: Prentice-Hall.
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  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
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