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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

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Spectral Density Prediction for Response of Nonlinear Gear Pairs under Random Excitation

Journal of Applied Nonlinear Dynamics 3(3) (2014) 283--294 | DOI:10.5890/JAND.2014.09.007

Jianming Yang$^{1}$; Ping Yang$^{2}$

$^{1}$ Faculty of Engineering and Applied Science, Memorial University of Newfoundland, St John’s, NL, Canada

$^{2}$ School of Mechanical Engineering, Jiangsu University, Zhenjiang, Jiangsu, P.R. China

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This paper investigates the dynamic response of a gear pair under random excitation from the view point of spectral density. Two methods are used to calculate the response spectral density function (SDF). The first method uses the statistical linearization (SL) technique to find an equivalent linear system to the original nonlinear one, then the response SDF is calculated with the equivalent linear system. While the second method regards the natural frequency of the system as a function of the response amplitude which is a random variable and its probability density function (PDF) is computed through stochastic averaging (SA). Then the response SDF is computed as a probabilistic averaging over the whole range of amplitude. Simulation result shows that both methods can predictthe resonant frequency very well and consistently in the case of weaknonlinearity. But with increasing of nonlinearity, the SDF predicted from the SL technique tends to be narrower than that from method II.


This work is supported financially by the IgniteR&D from Research & Development Corporation, Newfoundland and Labrador, Canada.


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