Free vibration of arches flexible in shear.

An analysis reported by Veletsos et al. (1972) concerning the free vibrational characteristics of circular arches vibrating in their own planes is considered. The analysis was based on a theory which neglects the effects of rotatory inertia and shearing deformation. A supplementary investigation is conducted to assess the effects of the previously neglected factors and to identify the conditions under which these effects are of practical significance or may be neglected. A simple approximate procedure is developed for estimating the natural frequencies of arches, giving due consideration to the effects of the previously neglected factors.