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A strongly nonlinear oscillator with nonlinear damping subject to narrow band random excitation is discussed. The deterministic and the stochastic responses are studied, respectively, applying the improved complex normal form method based on He’s energy balance method. The accuracy of detecting of the response frequency has been improved significantly. The behavior of steady state responses together with the stability is analyzed by the moment method. The numerical simulation results are consistent with theoretical analysis. When the noise intensity is small enough, the analytical result given by the moment method agrees with the simulation quite well.

Application of the Improved Complex Normal Form Method Based on He’s Energy Balance Method to a Noise Included Nonlinear Oscillator