Keywords: delamination, composite plate, finite element, structural health monitoring, modal analysis.

Structural studies to find defects (in particular delaminations) in composite plates have been very prevalent in the structural health monitoring field. In particular, delamination or debonding of adjoining plies is one of the most frequently encountered damage in composite structures. It can have originated during manufacture or during service-life arising from fatigue or impact.

The presence of delamination modifies the carrying capacity of the structure, leading to catastrophic consequences. Delamination is difficult to detect and developing efficient methods for its detection has been the object of several research lines in recent years.

Model based methods have been developed to avoid in-situ inspections of the structure. In addition, a large quantity of experiments can be spared to study these effects.

The present work studies the vibration of delaminated plates through the design, implementation and validation of a novel plate finite element. This is done with classical lamination plate theory in which delamination is considered in the kinematic equations through jump functions and additional degrees of freedom. From this model, a plate finite element is formulated, including the anisotropic tangent stiffness and mass matrices. The element allows the introduction of n_d delaminations through its thickness. The result is a simple quadrilateral element although with 5+(5×n_d) degrees of freedom per node.

Examples are studied and several mode shapes are obtained, with and without delamination, and in the latter for different sizes. A damage parameter is defined and used to differentiate delaminated and pristine mode shapes.

For beams, the curvature damage index is the most indicative, and only with a few modes the delamination seems to be detectable. As it is well known, eigenfrequences have no interest, because their differences are smaller than 3% in the higher modes. Two composite plates are also studied, but in this case the possibility of detection happens to be smaller; differences in eigenfrequences are practically zero. One difference with respect to beams is that curvatures are not always better than displacements to obtain damage indices.

Two kinds of delamination are studied. First, for large delaminations (>10%), a few modes seem to be enough for the detection. Second, for small delaminations (<10%) higher modes are required.

The future utility of this element is its inclusion in optimization processes to be used in more advanced damage detection techniques.

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