Date of Award
Periodic structures have been of particular interest to researchers and engineers due to their interesting vibrational characteristics leading to applications, namely acoustic filters, and waveguides. Many studies on the interaction of nearest neighbors have been performed. However, such studies are insufficient to understand the variation of band gaps and the maximum number of wave vectors for each frequency. The complex band structure obtained from the interaction beyond nearest neighbors can assist in the development of sophisticated acoustic technologies. This paper primarily emphasizes the study of such interactions with the development of mathematical models based on electrostatic forces, supported by the plots generated from MATLAB and COMSOL simulation. The electrostatic forces of attraction/ repulsion between charged cylinders in a periodic structure build the foundation of this research. The stiffness of the structure due to electrostatic interaction and the bandgap created due to stiffness would be discussed in detail using a mathematical model. The stiffness due to the mechanical properties of cylinders (cantilever beam) cannot be disregarded for a wholesome analysis. Thus, the effect of material stiffness in the band structure and the appropriate choice of material for fabrication of such periodic structure would be described in nutshell at the end of the paper. The result from this paper also paves way for the fabrication and experimentation of structures for similar interactions and interactions in 3D configuration.
Pathak, Sudesh, "Interaction Beyond Nearest Neighbor in Periodic Structures" (2022). Honors Theses. 2665.
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