Primary resonance of multiple degree-of-freedom dynamic systems with strong non-linearity using the homotopy analysis method

A homotopy analysis method (HAM) is presented for the primary resonance of multiple degree-of-freedom systems with strong non-linearity excited by harmonic forces. The validity of the HAM is independent of the existence of small parameters in the considered equation. The HAM provides a simple way to adjust and control the convergence region of the series solution by means of an auxiliary parameter. Two examples are presented to show that the HAM solutions agree well with the results of the modified Linstedt-Poincar, method and the incremental harmonic balance method.