Date of Award
3-2006
Document Type
Thesis
Degree Name
Master of Science
Department
Department of Aeronautics and Astronautics
First Advisor
Donald L. Kunz, PhD
Abstract
Hamilton's Law is derived in weak form for slender beams with closed cross sections. The result is discretized with mixed space-time finite elements to yield a system of nonlinear, algebraic equations. An algorithm is proposed for solving these equations using unconstrained optimization techniques, obtaining steady-state and time accurate solutions for problems of structural dynamics. This technique provides accurate solutions for nonlinear static and steady-state problems including the cantilevered elastica and flatwise rotation of beams. Modal analysis of beams and rods is investigated to accurately determine fundamental frequencies of vibration, and the simulation of simple maneuvers is demonstrated.
AFIT Designator
AFIT-GAE-ENY-06-M21
DTIC Accession Number
ADA449340
Recommended Citation
Leigh, Elliott J., "Simulation of a Moving Elastic Beam Using Hamilton's Weak Principle" (2006). Theses and Dissertations. 3566.
https://scholar.afit.edu/etd/3566