When material property geometry parameters and applied loads of
structure are assumed to be stochastic, four methods of nonlinear vibration are
proposed. The Newton method is applied to nonlinear vibration. Taylor expansion is
used to analyze nonlinear vibration. The perturbation technology is proposed to
compute nonlinear vibration. A modified iteration formula by the homotopy
perturbation method is presented to analyze nonlinear vibration.
Keywords: A modified iteration formula, Nonlinear vibration, The Newton
method, Taylor expansion, The perturbation technology.