Spectral analysis and structural response of periodic and quasi-periodic beams

Periodic structures have found a big interest in engineering applications because they introduce frequency band effects, due to the impedance mismatch generated by periodic discontinuities in the geometry, material, or boundary conditions, which can improve the vibroacoustic performances. However, the presence of defects or irregularity in the structure leads to a partial lost of regular periodicity (called quasi-periodic structure) that can have a noticeable impact on the vibrational and/or acoustic behavior of the elastic structure. The irregularity can be tailored to have impact on dynamical behavior. In the present paper, numerical studies on the vibrational analysis of one-dimensional finite, periodic, and quasi-periodic structures are presented. The contents deal with the finite element models of beams focused on the spectral analysis and the damped forced responses. The quasi-periodicity is defined by invoking the Fibonacci sequence for building the assigned variations (geometry and material) along the span of finite element model. Similarly, the same span is used as a super unit cell with Floquet-Bloch conditions waves for analyzing the infinite periodic systems. Considering both longitudinal and flexural elastic waves, the frequency ranges corresponding to band gaps are investigated. The wave characteristics in quasi-periodic beams, present some elements of novelty and could be considered for designing structural filters and controlling the properties of elastic waves.