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" Dynamics of Finite Phononic Crystals and Metamaterials "
Al Ba’ba’a, Hasan Baker Mohammad
Nouh, Mostafa
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Latin Dissertation
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| Language of Document
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English
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| Record Number
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1105244
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| Doc. No
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TLpq2304962651
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| Main Entry
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Al Ba’ba’a, Hasan Baker Mohammad
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Nouh, Mostafa
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| Title & Author
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Dynamics of Finite Phononic Crystals and Metamaterials\ Al Ba’ba’a, Hasan Baker Mohammad Nouh, Mostafa
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| College
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State University of New York at Buffalo
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| Date
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2019
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2019
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| Degree
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Ph.D.
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| Page No
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220
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| Abstract
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Phononic materials (PMs) are artificially engineered materials that exhibit a periodic variation in their mechanical or geometric properties which culminate in unprecedented bulk properties which are not readily available in naturally occurring materials. Owing to their unique ability to manipulate wave propagation within their medium, PMs have witnessed a spurt in research activity in the last few decades primarily due to the formation of frequency band gaps where wave propagation is effectively blocked without the use of dissipation mechanisms. The existence of band gaps in such optimally engineered materials is predicted based on the constitutive unit cell dynamics which automatically assume an infinitely long PM. The unit cell analysis provides the full potential of a PM, but does not guarantee the same performance in a finite PM comprising a number of unit cells; a lingering issue that has not been sufficiently addressed in literature. To address this shortcoming, this dissertation presents an analytical, computational, and experimental studies on finite PMs with its various types: Phononic Crystals (PCs) and Acoustic Metamaterials (AMs). The overarching theme of this dissertation is to understand band gap formation and evolution mechanisms in finite PMs for an arbitrary number of unit cells and mechanical/geometric properties for the PM types. In literature, band gaps have been classified into two main categories: Bragg scattering and local resonance band gaps, which correspond to PCs and AMs, respectively. To comprehend the band gap formation mechanisms, we adopt an approach based on systems theory to derive the end-to-end transfer function relating a periodic system's response (output) to an incident wave (input). Despite the challenges that this constraint poses, an essential criterion of the developed mathematical framework is to be entirely analytical and to provide closed-form solutions that can be readily extended to any set of arbitrary parameters and number of self-repeating cells. The transfer function analysis sheds light on the dynamics of finite realizations of periodic structures, and provides physical insights into the mechanism of band gap evolution as a function of inertial and elastic parameters, as well as different size and geometric variations. Another part of this dissertation involves the study of dissipative PMs using an energy based methodology to understand the pathways in the periodic structure as well as the rather complicated interplay between material dissipation and band gap mechanism. The structural intensity analysis (SIA) is used for this purpose and a two-dimensional plate-type AM structure is investigated numerically and experimentally. In addition, dissipative PMs have shown amplified damping ratios (known as metadamping) purely due to their intrinsic structural configuration. Based on these observations, we propose a novel configuration of periodic structures possessing hybrid attributes from two classes of PMs, namely PC and AM, which we refer to as the phononic resonator (PR). The optimal choice of mass and stiffness ratios serves as tunability metrics to lend the PR the characteristics of either a PC or an AM structure as well as the possibility of performing as a uniform lattice. These metadamping effects have also been studied for viscous and viscoelastic damping models, and the difference between these types have been highlighted. Based on the established understanding of band gap formation, we use control-theoretic methods for synthesizing a band gap-like behavior in monatomic (uniform) lattices at a prescribed frequency interval based on the established understanding of band gap formation. The input shaping approach is used to synthesize one or more band gaps that resemble either Bragg-scattering in PC or local resonance effects in AM. The presence of the artificial band gaps in the lattice's dispersion behavior is successfully verified using a spatiotemporal Fourier transform of the system's response which generates a contour relating the spatial and temporal frequencies, as well as using the end-to-end frequency response function. Finally, a polynomial chaos approach has been exploited to quantify uncertainties in wave dispersion and finite structure dynamics of the different types of PMs. Design guidelines for minimizing the effect of uncertainty and guaranteeing that the system performance closely resembles the nominal design characteristics have been illustrated and employed.
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Acoustics
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Mechanical engineering
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