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Structural Engineering and Mechanics
  Volume 13, Number 6, June 2002 , pages 713-730

Free vibrations of inclined arches using finite elements
Chucheepsakul S, Saetiew W

    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).
Key Words
    finite elements, free vibrations, inclined elastic arches, mode shapes
Chucheepsakul S, King Mongkuts Univ Technol, Dept Civil Engn, Bangkok 10140, Thailand
King Mongkuts Univ Technol, Dept Civil Engn, Bangkok 10140, Thailand

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