Free Vibration Analysis of Stepped Parabolic Arches with Timoshenko's Theory

Timoshenko 이론에 의한 불연속 변단면 포물선 아치의 자유진동 해석

The differential equations governing free, in-plane vibrations of stepped non-circuiar arches are derived as nondimensional forms including the effects of rotatory inertia, shear deformation and axial deformation. The governing equations are solved numerically to obtain frequencies and mode shapes. The lowest four natural frequencies and mode shapes are calculated for the stepped parabolic arches with hinged-hinged, hinged-clamped, and clamped-clamped end constraints. A wide range of arch rise to span length ratios, slenderness ratios, section ratios, and discontinuous sector ratios are considered. The effect of rotatory inertia and shear deformation on natural frequencies is reported. Typical mode shapes of vibrating arches are also presented.