Repeated resonances in folded-back beam structures

This paper investigates the interesting behaviour of a structure composed of identical Euler beams, joined together in a fan-folded configuration with one end clamped and the other end completely free. It is shown that when the structure comprises an even number of beams, all resonances occur in perfect pairs. When the structure comprises an odd number of beams, some resonances occur in perfect pairs in addition to resonances that coincide exactly with the natural frequencies of a single clamped–free beam unit. Moreover, irrespective of the number of beams present in the structure, resonances occur in clusters each one of them having a closed boundary at a clamped–free beam resonance and an open boundary at a free–free beam resonance. For consecutive clusters, these boundaries are determined in alternation by the resonances of free–free and clamped–free beams.