An Iteration Method for Single-Degree-of-Freedom Nonlinear Dynamical Equation

An approximate analytical approach based on Newton iteration method is presented for seeking the approximate analytical solutions of the nonlinear dynamical equation2s with single-degree-of-freedom. By this technology, the iteration operator L which may have an undetermined parameter can be both linear or a nonlinear one that can be settled. Furthermore, it has an unique technique which can be called as filtering function comparing with the harmonic balance method. This technique has also unified, simplified and developed the variational iteration method, the homotopy perturbation method, the parameterized perturbation method and the linear perturbation method. Using some nonlinear dynamical equations as examples, a convictive result has been achieved.