Natural frequency optimization of braided bistable carbon/epoxy tubes: Analysis of braid angles and stacking sequences

The natural frequency of cantilevered bistable carbon/epoxy reeled composite (BRC) slit tubes constructed from combinations of braided and unidirectional (UD) plies is optimized with respect to fiber orientation angles and laminate stacking sequences. BRC tubes have the same geometry as a carpenter's tape; however, they also have a second stable configuration in the coiled state, and it is considered likely that the coiled state diameter will be fixed by the geometry of the deployment mechanism or its housing. The optimization process uses the BRC coiled diameter as a constraint, and the maximum and minimum physically achievable braid angles as bounds. Both individual tubes, and a simple deployable solar array concept are analyzed. It is observed that the braid angle, rather than ply location in the stack is of greater importance when optimizing long slender or shallow BRCs, whereas both factors must be considered in shorter BRCs. The sensitivity of natural frequency and coiled diameter to braid angle perturbations indicates the importance of precision during manufacture.