KSCE Journal of Civil Engineering

, Volume 8, Issue 1, pp 43–48 | Cite as

Free vibrations of arches with inclusion of axial extension, shear deformation and rotatory inertia in Cartesian coordinates

  • Byoung Koo Lee
  • Tae Eun Lee
  • Dae Soon Ahn
Structural Engineering


The differential equations governing free vibrations of the elastic, parabolic arches with unsymmetric axes are derived in Cartesian coordinates rather than in polar coordinates. The formulation includes the effects of axial extension, shear deformation, and rotatory inertia. Frequencies and mode shapes are computed numerically for arches with clamped-clamped and hinged-hinged ends. The convergent efficiency is highly improved under the newly derived governing equations in Cartesian coordinates. The four lowest natural frequency parameters are reported as functions of four non-dimensional system parameters: the rise to chord length ratio, the span length to chord length ratio, the slenderness ratio and the shear parameter. Typical mode shapes of vibrating arches are also presented.


cartesian coordinates natural frequency axial extension shear deformation rotatory inertia 


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Copyright information

© KSCE and Springer jointly 2004

Authors and Affiliations

  1. 1.School of Civil, Environmental and Urban EngineeringWonkwang UniversityKorea
  2. 2.Department of Civil and Environmental EngineeringWonkwang UniversityKorea

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