Date of Award
9-16-2016
Document Type
Thesis
First Advisor
Jeongho Ahn
Committee Members
Jie Miao; William Paulsen
Call Number
LD 251 .S566t 2016 M38
Abstract
We consider a nonlinear hyperbolic fourth order partial differential equation and ordinary differential equation mathematically and numerically that describe the motion of cracked Euler-Bernoulli beams. We assume that the endpoints of the beams are clamped and a crack in the beams is modeled by a set of natural boundary conditions. The effect of the crack on the beams increases in time, which is seen from the damage function. The beams will oscillate transversely in space until they break at the point of the crack. The midpoint rule is applied to a discretized time domain. Fully discrete numerical schemes are proposed to approximate the displacement and velocity of the beams at each time step. Numerical experiments are performed using Mathematica and Matlab. Numerical results are presented and discussed.
Rights Management
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Recommended Citation
Mayfield, Jay, "Mathematical and Numerical Approaches to Cracked Euler-Bernoulli Beams" (2016). Student Theses and Dissertations. 649.
https://arch.astate.edu/all-etd/649
