Accurate analytical approximate solutions to general strong nonlinear oscillators

Anew approach is presented for establishing the analytical approximate solutions to general strong nonlinear conservative single-degree-of-freedom systems. Introducing two odd nonlinear oscillators from the original general nonlinear oscillator and utilizing the analytical approximate solutions to odd nonlinear oscillators proposed by the authors, we construct the analytical approximate solutions to the original general nonlinear oscillator. These analytical approximate solutions are valid for small as well as large oscillation amplitudes. Two examples are presented to illustrate the great accuracy and simplicity of the new approach.