In-Plane Vibrations of Curved Bars

Abstract

The in-plane free vibrations of curved bars with constant cross section, of which center lines are some plane curves are investigated by neglecting the rotatory inertia and the shear deformation. A rigorous method for solving the equations of motion is presented. 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 sine, catenary, hyperbola, parabola, cycloid and for an asymmetric elliptic arc bar with both ends clamped.