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.