Ricerc@Sapienza

We operate a perturbation approach on the finite field equations for clamped slender arches with compact symmetric cross-section and parabolic centre curve under a uniform line load parallel to their symmetry axis. We study small vibration superposed on the relevant stress, assumed of membrane nature. We find the fundamental angular frequency in terms of the aspect ratio of the arch and of the pre-load; the possibility of buckling is examined. This is a first step towards monitoring such structures, and evaluating pre-loads and structural integrity by dynamic measurements.

We study natural vibration of elastic parabolic arches, modeled as plane curved beams susceptible to elongation, shear, and bending, exhibiting small concentrated cracks. The crack is simulated by springs between regular chunks, with stiffness evaluated following stress concentration in usual crack opening modes. We evaluate and compare the linear dynamic response of the undamaged and damaged arch in nondimensional form. The governing equations are turned into a system of first-order differential equations that are solved numerically by the so-called matricant.