Free Vibration of Ogival Circular Arch

This study aims to analyze the free vibration of an ogival arch in which two symmetrical arched shapes are discontinuously met at the mid-arc. Differential equations governing the free vibration of an ogival circular arch were derived, where the rotatory inertia and shear deformation effects are included. The governing equations were numerically solved to calculate natural frequencies and mode shapes. In numerical solution methods, the symmetric and anti-symmetric boundary conditions at the mid-arc were focused rather than the boundary conditions of supported end due to the discontinuity of the mid-arc. For the first time, the free vibration problem for discontinuous arches, such as ogival arches, is solved in this study. Calculation results of this study for natural frequencies are compared well with those of the finite element method. The effects of various arch parameters on natural frequencies were highlighted and discussed in detail.