Vibrations of Curved Bars Perpendicular to Their Planes

概要

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We have researched the out-of-plane vibrations of curved bars with uniform cross section, of which center lines are some plane curves. Two general methods for solving the problems are presented: one is to use a variable, of which the relation to arc length represents the curvature and the other is to use the curvature expressed by arc length. As numerical examples, the frequencies and the mode shapes are shown in graphs for symmetric arc bars with clamped ends having the center lines in the form of ellipses, sines, catenaries, hyperbolas, parabolas and cycloids. And from the results, a general tendency in the out-of plane vibrations of curved bars is found.