Lowest Natural Frequencies of Elastic Hinged Arcs

Abstract

Approximate formulas are derived for the lowest natural frequencies of hinged elastic arcs having the center lines in the form of a circle, of a cycloid, of a catenary, and of a parabola in the case of vibrations occurring either in the plane of the initial curvature or in the plane perpendicular to the plane of the initial curvature of the arcs. Numerical results for the frequencies are presented in tabular and graphical form. The paper supplements previous published papers by the present authors in which the same problems were solved for the case of elastic built-in arcs.