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A new modification of homotopy analysis method (HAM) is proposed in this paper. The auxiliary differential operator is specifically chosen so that more than one secular term must be eliminated. The proposed method can capture asymmetric and period-2 solutions with satisfactory accuracy and hence can be used to predict symmetry-breaking and period-doubling bifurcation points. The variation of accuracy is investigated when different number of frequencies are considered.

A new modi¯cation of homotopy analysis method (HAM) is proposed for capturing asymmetric solutions of wire rope isolation systems. Analytical expressions of asymmetric solutions to wire rope isolation systems are obtained. A dynamic system with quadratic polynomial restoring force is investigated speci¯cally. Then the analytical results are applied to a single-degree-of-freedom (SDOF) system with wire rope vibration isolator to investigate the response curve and other dynamic characteristics. The analytical approximations match satisfactorily with the numerical results. The presented analytical approximation is a useful method to derive the response curves and examine limit cycles without resorting to numerical simulations.

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