Generalizing Modified Homotopy Perturbation Method to Study the Large Amplitude Vibration of Beams Subjected to an External Harmonic Excitation

Objectives: In present paper, large amplitude vibration behavior of an Euler-Bernoulli beam with immovable clampedclamped boundary conditions subjected to an external harmonic excitation resting on Pasternak foundation is investigated. Methods: Assuming the mid-plane stretching in the beam and using the Newton’s second law and then implementing the Galerkin’s method, the ordinary nonlinear differential equation is derived. Because of the large coefficient of the nonlinear term, the traditional perturbation methods based on the small coefficient of the nonlinear term lead to an invalid solution. Results: To solve the obtained strongly nonlinear non-homogeneous equation, the Modified Homotopy Perturbation Method (MHPM) is generalized. In order to validate the results of MHPM, some experimental tests carried out. Conclusion: The results show a good agreement between analytical and experimental data. Moreover, the time response of the first and second order generalized MHPM follows accurately the time response obtained by numerical solution.