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A cantilever beam built of fiber-resin composite material and damaged by heat is evaluated for its dynamic response using numerical methods. The goal of research is to produce a diagnostic process in which dynamic response can be used to estimate the severity of damage to the beam. Research proceeds from formulation of the continuous media equations for vibration in a multiply segmented beam, to the development of finite element models for the beam. It is discovered that the results of these two methods are qualitatively different from the predictions of a lumped system model, in that the lumped system predicts that frictional damping should reduce the dominant frequency of vibration while the more elaborated models indicate that damping may increase the dominant frequency. It is further discovered that the size and location of damage (the geometry) are equally as important as the local stiffness and damping of the damaged region (the material properties). The results indicate that the dominant frequency of dynamic response is not a sufficient symptom for complete diagnosis of damage in the beam.

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The effect of localized heat damage on the first natural frequency of fiber glass reinforced plastic is studied. The study is performed to determine the possibility of using natural frequency to evaluate the damage state of a composite. The natural frequency and its variation with the damage (size, location, and severity) are obtained using finite element analyses, continuum and lumped models. The results show that the natural frequency of composite specimen decreases with the growth of the damage size and increase of damage severity. However, its variation is much more sensitive to the damage size and location than to its severity. The natural frequency apparently does not change significantly with the number of damage spots as long as the total damage area is constant. A correlation between the natural frequency and the residual tensile strength of the composite is obtained, indicating its potential in predicting the residual strength of damaged composites.