Solution of sub, super, harmonic and combination type resonant excitations in nonlinear lumped parameter systems (Q1088041)

The author proposes a new perturbation procedure in order to approximate the transient and steady-state harmonic solutions of oscillatory systems defined by ordinary nonlinear differential equations. The procedure consists of a systematic combination of the well known concepts of multiple time scales and strained coordinates. It does not need any a priory knowledge of the solution form and thus leads to a more logical development of the overall solution including all the various types of resonances both damped and undamped. Several examples show the effectiveness of the method.