Analytical Treatment of In-Plane Parametrically Excited Undamped Vibrations of Simply Supported Parabolic Arches

[+] Author and Article Information
Dimitris S. Sophianopoulos

George T. Michaltsos

Structural Analysis and Steel Bridges, Civil Engineering Department, National Technical University of Athens, 42 Patision Str., Athens, 10682 Greece

J. Vib. Acoust 125(1), 73-79 (Jan 06, 2003) (7 pages) doi:10.1115/1.1521952 History: Received February 01, 2001; Revised April 01, 2002; Online January 06, 2003
Copyright © 2003 by ASME
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Geometry and sign convention of a simply supported parabolic arch
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Deformation of an arch element
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Deformed configuration of the arch
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Loads on an arch element
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Excitation frequency vs. excitation parameter plots for primary (n=1) and secondary (n=2,3) resonances, containing the regions of dynamic instability (shaded) and stability of the arch considered
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Mode shapes of the exemplary steel parabolic arch for the first three vibration modes
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Time series and phase trajectories corresponding to stable points S1–S4, as depicted in Fig. 5
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Time series and phase trajectories corresponding to unstable points U1–U3, as depicted in Fig. 5




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