Nonlinear free vibration of beams by one-dimensional and elasticity solutions

In this research, linear and nonlinear free vibration are examined. A three-dimensional rectangular parallelepiped free–free beam is studied based on the Ritz method. The equation of motion is derived depending on Hamilton's principle. A validation of the Ritz method formulation has been conducted by comparison with the Euler–Bernoulli beam theory. The impact of three-dimensional beam length has been investigated as well. In terms of nonlinear analysis, a two-dimensional clamped–clamped beam was studied. Total Lagrange formulation is adopted for the elasticity method based on the Green–Lagrange strain tensor and second Piola–Kirchhoff stress tensor. The outcomes of the approximated method have been compared by using the nonlinear Euler–Bernoulli theory depending on the Hermite and Lagrange interpolations. The solutions of both theories are computed according to the direct iteration method. Poisson's ratio effect is studied with two assumptions, as well as the impact of the Gauss evaluations.

Name thesis:degree_name

Master of Science (M.S.)

Level thesis:degree_level

Masters

Discipline thesis:degree_discipline

Civil and Environmental Engineering

Grantor dc:publisher

Colorado State University. Libraries

Year dc:date.issued

2018

Authors dc:creator

• Asiri, Abdullah N., author
• Heyliger, Paul, advisor
• Chen, Suren, committee member
• O'Reilly, Mike, committee member

Statement dc:rights

• Copyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.

Language dc:language.iso

eng, English

Identifier URI

https://doi.org/10.25675/3.06343

OAI identifier oai:identifier

oai:mountainscholar.org:10217/193193