회전관성, 전단변형 및 축변형을 고려한 변단면 원호아치의 자유진동

Free Vibrations of Tapered Circular Arches Considering Rotatory Inertia. Shear Deformation and Axial Deformation

This paper deals with the free vibrations of circular arches with variable cross-section. The differential equations governing free, in-plane vibrations of tapered circular arches, including the effects of rotatory inertia, shear deformation and axial deformation, are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for the quadratic arches with hinged-hinged and clamped-clamped end constraints. Three general taper types for a rectangular section are considered. The lowest four natural frequencies and mode shapes are presented over a range of non-dimensional system parameters： the subtended angle, the slenderness ratio and the section ratio.