Investigation for the analysis of the vibrations of quasi-periodic structures

Periodic structures are well known for the possibility to exhibit band gap effects. This work aims at investigating vibration behaviors of quasi-periodic structures. In this paper, the quasi-periodic structure is defined as a type of beam with an impedance mismatch generated by Fibonacci orders with non-symmetrical translation in geometry, acting as a waveguide. Two types of quasi-periodicity are considered, namely finite, and infinite Fibonacci sequences using super unit cell. Considering flexural elastic waves in above mentioned quasi-periodic models, the frequency ranges corresponding to band gaps are investigated, using either spectral analysis of infinite structures or frequency response functions of finite structures. Fibonacci beams exhibit multi stop bands with short widths in different frequency ranges, whereas periodic and its super unit cells-based structures have only one stop band frequency with larger frequency extension.