Date of Award

Winter 2017

Project Type


Program or Major

Applied Mathematics

Degree Name

Master of Science

First Advisor

Marianna A. Shubov

Second Advisor

Marianna A. Shubov

Third Advisor

Mark Lyon


We derive herein approximate spectra for three dierent models of transversely vibrating, beams. Each model consists of a system of partial dierential equations (PDEs) with various, boundary conditions. The three models that we consider are the Euler-Bernoulli model, the, Rayleigh model, and the Timoshenko model. We rst discuss a brief history of the models, before delving into obtaining the spectral equations for each beam model under dierent, boundary conditions. Lastly, we present asymptotic approximations of some of the various, spectral equations we found from each model.