NATURAL FREQUENCIES OF NON-CIRCULAR ARCHES WITH ROTATARY INERTIA AND SHEAR DEFORMATION

The differential equations governing free, in-plane vibrations of non-circular arches, including the effects of rotatory inertia, shear deformation and axial deformation, are derived and solved numerically to obtain frequencies and mode shapes. The lowest four natural frequencies are calculated for the parabolic, elliptic and sinusoidal geometries with hinged–hinged, hinged–clamped, and clamped–clamped end constraints. A wide range of arch rise to span length ratios, slenderness ratios, and two different values of shear parameter are considered. The agreement with results determined by means of a finite element method is good from an engineering viewpoint.