Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function

Author

Daniel Siebel-Cortopassi, University of South Florida

Graduation Year

2022

Document Type

Thesis

Degree

M.A.

Degree Name

Master of Arts (M.A.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Sherwin Kouchekian, Ph.D.

Committee Member

Ivan Rothstein, Ph.D.

Committee Member

Boris Shekhtman, Ph.D.

Committee Member

Joel Rosenfeld, Ph.D.

Keywords

Decentralized control, Coupled harmonic oscillators, Microcantilevers, Delay differential equations, Stable regions

Abstract

A coupled delay-feedback system of two cantilevers can yield greater sensitivity than that of asingle cantilever system, with potential applications in atomic force microscopy. The Lambert W-function analysis concept for delay differential equations is used to more accurately model the behavior of specific configurations of these cantilever systems. We also use this analysis concept to find parameters which yield stability for greater parameter ranges, of the delay differential equations. The Q factor, or quality factor, is the ratio of energy stored in the system, to the energy lost per fixed oscillation/movement cycle. Having stability of the cantilevers corresponds to the physical system having a better Q factor and better sensitivity.

Scholar Commons Citation

Siebel-Cortopassi, Daniel, "Stability Analysis of Delay-Driven Coupled Cantilevers Using the Lambert W-Function" (2022). USF Tampa Graduate Theses and Dissertations.
https://digitalcommons.usf.edu/etd/9462