Response analysis of Van der Pol oscillator subjected to harmonic and random excitations

The response of the Van der Pol oscillator subjected to combined harmonic and random excitations is investigated by a technique combining two excellent methods, namely the stochastic averaging method and the equivalent linearization method. The original equation is averaged by the stochastic averagi...

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Bibliographic Details
Published in:Probabilistic engineering mechanics 2014-07, Vol.37, p.51-59
Main Authors: Anh, N.D., Zakovorotny, V.L., Hao, D.N.
Format: Article
Language:English
Subjects:
Averaging method
Equivalence
Equivalent linearization
Harmonic excitation
Harmonics
Linearization
Mathematical analysis
Mathematical models
Nonlinearity
Oscillators
Random excitation
Stochasticity
Van der pol
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Summary:The response of the Van der Pol oscillator subjected to combined harmonic and random excitations is investigated by a technique combining two excellent methods, namely the stochastic averaging method and the equivalent linearization method. The original equation is averaged by the stochastic averaging method at first. Then the resulting nonlinear averaged equations are linearized by the equivalent linearization method so that the equations obtained can be solved exactly by the technique of auxiliary function. The mean square response of the Van der Pol oscillator is computed algebraically and compared to the ones obtained by numerical simulation and by technique combining methods of stochastic averaging and equivalent non-linearization. The results show that the proposed technique gives a good prediction on mean square responses of the Van der Pol oscillator. In addition, the proposed technique can be applied to other nonlinear systems for it does not require any special conditions, and it can be improved by advanced optimization criteria of the equivalent linearization method. •Non-autonomous and random Van der Pol oscillator is studied by new technique.•Two coupling random nonlinear equations are solved by a new approach.•Results are computed algebraically and compared to two other methods.•The proposed technique is validated in certain ranges of values of system parameters.•The paper opens up new possibilities to study general non-autonomous nonlinear systems.
ISSN:0266-8920
1878-4275
DOI:10.1016/j.probengmech.2014.05.001