Sub-harmonic resonances of periodic parameter excited oscillators with the absolute value items

An analytic approach based on the homotopy analysis method (HAM) is proposed to study the sub-harmonic resonances of highly nonlinear periodic parameter excited oscillating systems with absolute value terms. The non-smoothness of absolute value terms is handled by means of an iteration approach with Fourier expansion. Two typical examples are employed to illustrate the validity and flexibility of this approach.