Analytical and differential quadrature results for vibration analysis of damaged circular arches

The present paper focuses on in-plane linear free vibrations of circular arches, in undamaged and damaged configurations. For the model herein utilized, the equations of motion, in terms of displacements and rotation, take into account shearing and axial deformations and rotary inertia. The cracked section of the arch is modeled with an elastic spring. An exact analytical method of solution and an approximate numerical one are presented. The first method solves the fundamental system in closed form, by means of a characteristic polynomial; the second one is based on a simple and efficient differential quadrature and domain decomposition technique. Natural frequencies and mode shapes are computed for some significant cases, showing very good agreement between the two approaches.