Out-of-plane free vibrations of curved beams with variable curvature

The differential equations governing out-of-plane free vibrations of the elastic, horizontally curved beams with variable curvature are derived and solved numerically to obtain natural frequencies and mode shapes for parabolic, sinusoidal and elliptic beams with hinged–hinged, hinged–clamped, and clamped–clamped end constraints, in which the effects of the rotatory and torsional inertias and shear deformation are included. Experimental measures of frequencies for several laboratory-scale parabolic models serve to validate the theoretical results.