Title

Lie Groups and Euler-Bernoulli Beam Equation

Author

Medeu Amangeldi, Illinois State UniversityFollow

Date of Award

3-30-2021

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Department of Mathematics

First Advisor

George Seelinger

Abstract

Lie groups approach in differential equations was a breakthrough subject in the late nineteenth century. Sophus Lie, a Norwegian mathematician, introduced the systematic approach to study the solutions of differential equations. The main goal of this thesis is to study, using Lie's approach, the Euler-Bernoulli beam equation subject to swelling force, the fourth-order nonlinear differential equation used to describe the beam deflection under the swelling force. In particular, we will classify the symmetry groups of this equation, obtain several reductions, and demonstrate both analytical and numerical solutions.

Comments

Imported from Amangeldi_ilstu_0092N_11924.pdf

Recommended Citation

Amangeldi, Medeu, "Lie Groups and Euler-Bernoulli Beam Equation" (2021). Theses and Dissertations. 1349.
https://ir.library.illinoisstate.edu/etd/1349

DOI

https://doi.org/10.30707/ETD2021.20210719070603170105.99

Page Count

64