Structural models for the evaluation of eigen-properties in damaged spatial arches: a critical appraisal

The paper considers the eigen-properties of spatial arch structures in both undamaged and damaged configurations. In the literature, several models have been proposed for modelling damage, mainly in beam-like structures, based on the concepts of equivalent elastic weakened section, for concentrated damage, or stiffness reduction influence area, for distributed damage. In damage identification procedures, it is needed to numerically represent the actual structure in which a reliable damage model has to be assumed. An unsuitable damage representation may lead to wrong or misleading results that, although consistent with the assumed model, could be not representative of the actual unhealthy condition of the structure. In this paper, focusing the attention on spatial Timoshenko arches, the eigen-properties of the undamaged and the damaged structure are exactly evaluated, consistent with an assumed continuous model, and compared to the corresponding results provided by several detailed finite element simulations based either on mono- or three-dimensional models. In the assumed continuous model, the damage is represented by considering an appropriate reduction, in a certain zone, in the arch cross section. The comparison with the widely adopted spring equivalent model is also made. A comparative parametric study is developed showing the role of damage on the natural frequencies of vibration of spatial arches and allowing to point out some ambiguous results that may lead to false inverse problem solutions.