Effects of cables damage on vertical and torsional eigenproperties of suspension bridges

This paper presents a continuum model for the nonlinear coupled vertical and torsional vibrations of suspension bridges with arbitrary damage in one main cable and, after pursuing a suitable linearization of the equations of motion, an investigation of damage effects on modal parameters. Damage is modeled as a diffused loss of cross-section representing the typical effect of fretting fatigue and it is introduced in the formulation by enforcing relevant literature results providing analytical solution for the static response of damaged suspended cables. The coupled nonlinear equations of motion of the damaged bridge, including the effects of shear deformation, rotary inertia and warping of the cross-section of the girder, are derived by application of Hamilton׳s principle. In this way, the equations of motion available in the literature for undamaged suspension bridges are generalized to the presence of arbitrary damage in one main cable and the resulting eigenfrequencies and eigenfunctions are derived in an analytical fashion. An extensive parametric investigation is finally presented to discuss damage effects on eigenfunctions and eigenfrequencies under variation of practically meaningful parameters.