Date of Award
6-19-2026
Document Type
Thesis
Degree Name
Mathematics, MS
First Advisor
William Paulsen
Committee Members
Jie Miao; Suzanne Melescue
Abstract
Cell phone towers, utility poles, and traffic signal poles all use hollow, tapered beams as their main structural element. Because these structures are tall and exposed to wind forces, understanding their vibration behavior is important for ensuring stability and safety. We will use the Exterior Matrix Method to analyse a single beam, which can be used to analyse compound structures involving tapered beams. First, we find the system of four equations satisfied by the tapered beam, which can be converted to a 4 x 4 matrix. Then we find the exterior matrix, which is a 6 x 6 matrix, corresponding to a system of 6 equations with 6 variables. By solving these 6 equations approximately, we derive the exterior matrix for the tapered beam structure. The advantage of going from 4 dimensions to 6 dimensions is that we can use the same matrix to analyse compound structures involving several tapered beams or apply different end conditions such as a load at the end of the beam. The analysis also shows that the thickness of the beam has little effect on the vibration behavior, meaning it can be neglected in the vibration model.
Rights Management
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Kaur, Simranjit, "Vibrations Of Tapered Beam Via the Exterior Matrix Method" (2026). Student Theses and Dissertations. 1179.
https://arch.astate.edu/all-etd/1179
