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A theoretical and experimental investigation on large amplitude free vibration behavior of a pretensioned beam with clamped–clamped ends using modified homotopy perturbation method

In this study, large amplitude free vibration behavior of a pretensioned Euler–Bernoulli beam is investigated both theoretically and experimentally. The Hamilton's principle is used to derive the beam governing equation of motion. By implementing the Galerkin's method and assuming the clamped–clamped boundary condition, the partial differential equation is converted to an ordinary nonlinear differential equation. Because of the large coefficient of the nonlinear term, the new homotopy perturbation method proposed by He, is modified to solve the governing nonlinear equation. Comparing the first- and the second-order approximate solutions of the modified homotopy perturbation method (MHPM) and those available in the literature demonstrates that the second-order MHPM leads to a more accurate solution which is valid for a wide range of the vibration amplitudes. The results have been validated by the experimental tests and the MHPM method. Also, the results show that an increase in the vibration amplitude and/or the pretension load increases the fundamental resonance frequency ratio. Besides, it would decrease with increasing the beam slenderness ratio.