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http://dx.doi.org/10.5050/KSNVN.2002.12.12.970

Free Vibrations of Arches in Cartesian Coordinates  

Lee, Byoung-Koo (School of Architectural Engineering, Wonkwang University)
Lee, Yong-Soo (Department of Architectural Interior Design, Chongin University)
Kim, Il-Jung (Graduate School, Wonkwang University)
Choi, Kou-Moon (School of Civil and Environmental Engineering, Wonkwang University)
Publication Information
Transactions of the Korean Society for Noise and Vibration Engineering / v.12, no.12, 2002 , pp. 970-978 More about this Journal
Abstract
The differential equations governing free vibrations of the elastic arches with unsymmetric axis are derived in Cartesian coordinates rather than in polar coordinates. in which the effect of rotatory inertia is included. Frequencies and mode shapes are computed numerically for parabolic arches with both clamped ends and both hinged ends. Comparisons of natural frequencies between this study and SAP 2000 are made to validate theories and numerical methods developed herein. The convergent efficiency is highly improved under the newly derived differential equations in Cartesian coordinates. The lowest four natural frequency parameters are reported, with and without the rotatory inertia, as functions of three non-dimensional system parameters the rise to chord length ratio. the span length to chord length ratio, and the slenderness ratio. Also typical mode shapes of vibrating arches are presented.
Keywords
Cartesian Coordinates; Free Vibration; Harmonic Motion; Arch; Mode Shape; Natural Frequency; Rotatory Inertia; Unsymmetric Axis; Variable Curvature;
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