Date of Award
Spring 2024
Project Type
Dissertation
Program or Major
Applied Mathematics
Degree Name
Doctor of Philosophy
First Advisor
Marianna Shubov
Second Advisor
Mark Lyon
Third Advisor
John Gibson
Abstract
A piezoelectric energy harvester is a device that utilizes the properties of piezoelectric materials to convert mechanical strain energy into electric energy. The present work is concerned with the asymptotic spectral analysis of a piezoelectric harvester extracting energy from the mechanical vibration of a coupled bending-torsion beam. After placing the model in the appropriate operator setting, we prove that the addition of piezoelectric energy harvesting constitutes a weak perturbation of the underlying beam dynamics, in the sense that the model’s piezoelectric parameters do not appear in the first two orders of magnitude of the asymptotic approximation of the governing operator’s spectrum. In addition, we show that the leading-order term of the spectrum’s approximation consists of a two-branch structure, and that a similar structure is retained to second order by an infinite subset of the spectrum. Finally, we propose numerical experiments that will complement the asymptotic results, helping expand their applicability.
Recommended Citation
Vales, Chris, "Asymptotic spectral analysis of a coupled bending-torsion beam energy harvester" (2024). Doctoral Dissertations. 2847.
https://scholars.unh.edu/dissertation/2847