Abstract: A strongly cubic nonlinear forced vibration system with single degree of freedom is investigated by means of homotopy analysis method(HAM). Different from other approximate computational method, the HAM is totally independent of small physical parameters, and thus is suitable for most nonlinear problems. The HAM provides us with a great freedom to choose base functions of solution series, so that a nonlinear problem may be approximated more effectively. The HAM adjusts and controls progression solution convergence region and the convergence rate through the introduction of auxiliary parameters and auxiliary functions. Therefore it opens up a new approach to the solution of analytical approximation of non-linear problems, and is especially suitable for strong non-linear problems. The computation results indicate that this method can not only solve the steady state solution but also calculate the unsteady state solution, and has good computational accuracy.

Key words: Forced vibration, Homotopy analysis method, Primary resonance, Single degree of freedom, Strong nonlinearity, continuous wavelet transform, correlated kurtosis, optimal wavelet scales cyclic spectrum, rolling element bearing, cyclic periodogram