Date of Award
12-7-2017
Document Type
Thesis
Degree Name
Mathematics, MS
First Advisor
William Paulsen
Committee Members
Jeongho Ahn; Jie Miao
Call Number
LD 251 .A566t 2017 A56
Abstract
We analyze the in-plane vibrations of a structure consisting of several Timoshenko beams joined together non-collinearly. We also consider the possibility of adding dissipative dampers in the structure. Using the exterior matrix method, we nd that the solution matrix can be expressed as a perturbation series over a small parameter and that the leading term of this series gives the solution to the Euler-Bernoulli beam equation. We then show how the exterior matrix method can be used to nd the eigenfunctions, via adding a small dash-pot at an arbitrary point in the structure, and seeing how much this dash-pot affects the eigenfrequencies. We prove that the effect on the eigenfrequency is proportional to the square of the largest displacement from the vibration in the direction of the dash-pot.
Rights Management
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Annamalai, Prabu, "Analyzing Non-Colinearly Coupled Timoshenko Beams Via the Exterior Matrix Method" (2017). Student Theses and Dissertations. 546.
https://arch.astate.edu/all-etd/546
