Honors Theses

Date of Award

Spring 5-7-2022

Document Type

Undergraduate Thesis

Department

Mechanical Engineering

First Advisor

Farhad Farzbod

Second Advisor

Taiho Yeom

Third Advisor

Tejas Pandya

Relational Format

Dissertation/Thesis

Abstract

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.

Accessibility Status

Searchable text

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.