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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 238714, 9 pages
Research Article

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

School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300192, China

Received 8 December 2014; Revised 8 April 2015; Accepted 19 April 2015

Academic Editor: P. Balasubramaniam

Copyright © 2015 Gen Ge and Zheng Chao Yun. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.