Abstract
The differential equations governing the free vibrations of elastic, horizontally curved beams with unsymmetric axes were derived from Cartesian coordinates rather than polar coordinates, in which the effect of torsional inertia is included. Frequencies and mode shapes were computed numerically for parabolic curved beams with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 were made to validate theories and numerical methods developed herein. The convergent efficiency significantly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters were reported, with and without torsional inertia, as functions of three non-dimensional system parameters: the horizontal rise to chord length ratio, the span length to chord length ratio, and the slenderness ratio. Typical mode shapes of vertical displacement were also presented.
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The manuscript for this paper was sumbitted for review on August 12, 2002.
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Lee, BK., Lee, TE. & Ahn, DS. Free vibrations of horizontally curved beams with unsymmetric axes in Cartesian coordinates. KSCE J Civ Eng 7, 147–152 (2003). https://doi.org/10.1007/BF02841973
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DOI: https://doi.org/10.1007/BF02841973