Nonlinear free vibration of beams by one-dimensional and elasticity solutions
Date
2018
Authors
Asiri, Abdullah N., author
Heyliger, Paul, advisor
Chen, Suren, committee member
O’Reilly, Mike, committee member
Journal Title
Journal ISSN
Volume Title
Abstract
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.