2026-09-20T01:13:23Zhttps://api.mountainscholar.org/server/oai/requestoai:mountainscholar.org:10217/1931932025-12-30T03:33:14Zcom_10217_100532com_10217_100000com_10217_100369com_10217_100303col_10217_100538col_10217_100381
Asiri, Abdullah N., author
Heyliger, Paul, advisor
Chen, Suren, committee member
O'Reilly, Mike, committee member
2019-01-07T17:19:40Z
2019-01-07T17:19:40Z
2018
Asiri_colostate_0053N_15230.pdf
https://hdl.handle.net/10217/193193
https://doi.org/10.25675/3.06343
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.
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masters theses
English
eng
Colorado State University. Libraries
2000-2019
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Nonlinear free vibration of beams by one-dimensional and elasticity solutions
Text
Master of Science (M.S.)
Masters
Civil and Environmental Engineering
Colorado State University
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