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 ...
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