Periodicity and quasi-periodicity effects on vibration band gaps: numerical investigations on one-dimensional structures

Periodic structures have found a big interest in engineering application because they introduce frequency band effects due to the impedance mismatch generated by periodic discontinuities in the geometry, material, or boundary conditions. Adding periodicity to structures leads to wave mode interaction, which generates pass-and stop-bands. The frequencies at which stop-bands occur are related to the periodic nature of the structure. The presence of defects or irregularity in the structure leads to a partial loss of regular periodicity (quasi periodic structure) that can have a noticeable impact on the vibrational and/or acoustic behavior of the elastic structure. The aim of this study is to analyze the dynamic behaviors of periodic and quasi-periodic structures, and to investigate where band gaps appear in the frequency range. First, the behavior of an infinite periodic structure through the dispersion diagrams is studied compared with the results obtained through the Carrera Unified Formulation (CUF). Then, numerical studies on different beams are done to compare band gaps position at different periodic and quasi-periodic sequences.