Eigenproperties of suspension bridges with damage

The vertical vibration of suspension bridges with a damage in the main cables is studied using a continuum formulation. Starting from a model for damaged suspended cables recently proposed in the literature, an improved expression for the dynamic increment of cable tension is derived. The non-linear equation of motion of the damaged bridge is obtained by extending this model to include the stiffening girder. The linear undamped modal eigenproperties are then extracted, in closed-form, from the linearized equation of motion, thus generalizing to the presence of an arbitrary damage the expressions known from the literature for undamaged suspension bridges. The linear dynamics of the damaged bridge reveals to be completely described by means of the same two non-dimensional parameters that govern the linear dynamics of undamaged bridges and which account for the mechanical characteristics of both the main cable and the girder, with the addition of three non-dimensional parameters characterizing damage intensity, position and extent. After presenting the mathematical formulation, a parametric analysis is conducted with the purpose of investigating the sensitivity of natural frequencies and mode shapes to damage, which, in fact, is a crucial point concerning damage detection applications using inverse methods. All through the paper, systematic comparisons with finite element simulations are presented for the purpose of model validation.