Vibration characteristics of fibrous composites with damage

A micromechanical model is developed in order to study the vibration characteristics of fibrous composites with damage. Damage is taken in the form of either a broken fiber of a matrix crack normal to the fiber direction. The unidirectionally reinforced periodic composite, when vibrating in the longitudinal (fiber) direction, is modeled as a concentric cylindrical system subjected at its outer boundaries to vanishing radial displacement and shear stress. Guided by the symmetry and the fiber-matrix interface continuity conditions, an approximate radial dependence of some of the field variables is first assumed. The two-dimensional field equations that hold in both the fiber and the matrix, together with their interface conditions, are then reduced to a quasi-one-dimensional system which automatically satisfies all interface and boundary conditions. The simplified model is applied to the study of the vibration characteristics of the composite with and without damage. The cases of broken fibers and cracked matrix are treated by invoking stress-free conditions at the crack faces. The dependence of the resonance frequencies and mode shapes on the nature and location of the damage is exploited. Significant reduction in the values of resonance frequencies can be realized for damage located close to the center of the composite system.