On Approximate Analytical Solutions of Nonlinear Vibrations of Inextensible Beams Using Parameter-Expansion Method

In this work, an analytical method, which is referred to as Parameter-expansion Method is used to obtain the exact solution for the problem of nonlinear vibrations of an inextensible beam. It is shown that one term in the series expansion is sufficient to obtain a highly accurate solution, which is valid for the whole domain of the problem. A comparison of the obtained the numerical solution demonstrates that PEM is effective and convenient for solving such problems. After validation of the obtained results, the system response and stability are also discussed.

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