Structural Engineering and Mechanics

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Free vibrations of inclined arches using finite elements

  • Chucheepsakul, Somchai (Department of Civil Engineering, King Mongkut's University of Technology Thonburi) ;
  • Saetiew, Wasuroot (Department of Civil Engineering, King Mongkut's University of Technology Thonburi)
  • Received : 2001.06.20
  • Accepted : 2002.04.08
  • Published : 2002.06.25
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Abstract

This paper presents a finite element approach for determining the natural frequencies for planar inclined arches of various shapes vibrating in three-dimensional space. The profile of inclined arches, represented by undeformed centriodal axis of cross-section, is defined by the equation of plane curves expressed in the rectangular coordinates which are : circular, parabolic, sine, elliptic, and catenary shapes. In free vibration state, the arch is slightly displaced from its undeformed position. The linear relationship between curvature-torsion and axial strain is expressed in terms of the displacements in three-dimensional space. The finite element discretization along the span length is used rather than the total are length. Numerical results for arches of various shapes are given and they are in good agreement with those reported in literature. The natural frequency parameters and mode shapes are reported as functions of two nondimensional parameters: the span to cord length ratio (e) and the rise to cord length ratio (f).

Keywords

Acknowledgement

Supported by : Thailand Research Fund (TRF)

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