Abstract
The transverse vibration solution for both uniform and non-uniform (variable cross-section) beams, with homogeneous or non-homogeneous (such as composites) linear elastic material properties has been widely discussed and is well documented. However, spatial variations in material properties due to history-dependent damage have not been previously considered. In this paper, the internal state variable concept is introduced to account for the cumulative stress-induced damage in a simple composite beam structure resulting from a fatigue-type loading of several hundred thousand cycles. Furthermore, the transverse vibration solution based on the history-dependent material is presented for a simple beam.
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