FREE VIBRATIONS OF FRAME STRUCTURES ADOPTING FUNCTIONALLY GRADED MATERIALS FOR DAMAGE MODELLING

The effects of the presence of damage in the free vibrations of structures have been widely in-vestigated in the scientific literature adopting several strategies to model the damage. Most of the studies consider a concentrated reduction of the stiffness of the structural member due to damage still maintaining the hypothesis of homogeneous material. Anyway, the mechanical characteristics of the damaged portion of the beam cannot be considered homogeneous for ex-ample when an external corrosion of the material occurs. In the present study the change of mechanical characteristics in the damaged portion of a structural element has been originally modelled by means of functionally graded materials which allow to introduce a smooth change in the material properties. In particular, the presence of damage is accounted for by means of the introduction of a beam element modelled as functionally graded, in which the material properties vary symmetrically across the height of the section with respect to the centroid. To simulate material degradation due to damage, it is assumed that the inner material is stiffer than the outer material. Since the damaged elements have a shorter length compared to the overall structural members, the effect of shear deformation is accounted for using the Timoshenko beam model. The proposed damage modelling approach is applied to framed structures in presence of con-centrated damage following the exact approach of the dynamic stiffness method in conjunction with the Wittrick and Williams algorithm. Numerical simulations have been carried out, vary-ing the properties of the damaged element, and comparisons have been made with other com-monly used damage models, such as the hinge with rotational spring and the reduction of the cross-sectional dimensions.