Symmetric free vibration of cracked arches of rigid discrete blocks

Abstract

The paper investigates the energy- and amplitude-dependent natural periods of symmetrically cracked semi-circular arches, which are loaded by their self-weight and horizontal support displacement. The cracks appear due to previous static effects. Symmetric free vibration of the arches is under analysis. The symmetry condition results in an SDoF system, but the latter purpose of the authors is to analyse nonsymmetric modes with an MDoF model.To analyse the problem an energy-based approach is developed. The motion of a structure consists of states with nonlinear vibrations, each of which has constant energy content. Between these phases inelastic impacts occur, which have effect only on the velocity field, but have no effect on the displacements, because the time duration of the impacts is assumed to be zero.In the work the position of the cracks and other geometrical parameters are under examination and the energy-, amplitude- and support displacement magnitude-dependent natural periods are obtained. These results may help to monitor the historical buildings structural safety, because with the measured natural period and amplitude one can determine the safety of the structure.