Modeling and analysis of a cracked composite cantilever beam vibrating in coupled bending and torsion

The coupled bending and torsional vibration of a fiber-reinforced composite cantilever with an edge surface crack is investigated. The model is based on linear fracture mechanics, the Castigliano theorem and classical lamination theory. The crack is modeled with a local flexibility matrix such that the cantilever beam is replaced with two intact beams with the crack as the additional boundary condition. The coupling of bending and torsion can result from either the material properties or the surface crack. For the unidirectional fiber-reinforced composite, analysis indicates that changes in natural frequencies and the corresponding mode shapes depend on not only the crack location and ratio, but also the material properties (fiber orientation, fiber volume fraction). The frequency spectrum along with changes in mode shapes may help detect a possible surface crack (location and magnitude) of the composite structure, such as a high aspect ratio aircraft wing. The coupling of bending and torsion due to a surface crack may serve as a damage prognosis tool of a composite wing that is initially designed with bending and torsion decoupled by noting the effect of the crack on the flutter speed of the aircraft.