Timorian, Safiullah (2020) Investigation for the analysis of the vibrations of quasi-periodic structures. [Tesi di dottorato]

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In this thesis, the definition and effects of quasi-periodicity in periodic structure are investigated. More importantly, the presence of irregularity in periodic structures and its significant impact in vibroacoustic responses of elastic systems are analyzed. In the extant literature, it has already shown that a sandwich panel, optimized for vibroacoustic performance with added random properties of the core, can exhibit stop band characteristics in some frequency ranges. Therefore, an additional target can exist in framing the abovementioned property under the Wave Finite Element Method (WFEM) for resulting in some design guideline. In this investigation, (1) the numerical studies of the vibrational analysis of 1D finite, periodic, and quasi-periodic beams are presented. The research’s content deals with the finite element models of beams focusing on 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 the finite element model in one direction. Similarly, the same span is used as a super unit cell with WFEM for analyzing the infinite periodic systems. (2) Variation method with a developed algorithm is considered to find the most efficient geometrical impedance mismatch of unit cells for vibration control. (3) Numerical studies and experimental measurements on 2D periodic and quasi-periodic lattices are thus performed. Experimental validations are per- formed by comparing the numerical quasi-periodic model with a prototype manufactured by laser machining. Based on the major findings, and considering both longitudinal and flexural elastic waves in 1D beams, the frequency ranges corresponding to band gaps are investigated. In the 2D structures, the wave characteristics in the quasi-periodic lattice introduce the possibility of designing wider frequency stop bands in low frequency ranges, and presents some elements of novelty; moreover, they can be considered for designing structural filters and controlling the properties of elastic waves. The results obtained in this study show that the beams with Fibonacci and panels with Thue-Morse characteristics can improve performances in terms of attenuation level without weight penalty, which can be an asset for meta-materials.

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