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Prediction of periodic motion plays a key role in understanding dynamical behavior of nonlinear systems and is also an essential prerequisite for identifying the pattern of their bifurcations and chaos.Among analytical methods the Harmonic Balance method(HBM)was considered one of the powerful methods that are able to give predictions of periodic motions of strong nonlinear systems.For many practical nonlinear problems,computational efficiency is as important as accuracy,which means the efficiency of the total analytical methods such as HBM should be improved.