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Feng, G., Xu, W., Rong, H. and Wang, R. (2009) Stochastic Responses of Duffing-Van der Pol Vibro-Impact System under Additive and Multiplicative Random Excitations. International Journal of Non-Linear Mechanics, 44, 51-57.
https://doi.org/10.1016/j.ijnonlinmec.2008.08.013

has been cited by the following article:

• TITLE: Random Response of a Strongly Nonlinear Oscillator with Internal and External Excitations

  AUTHORS: Claudio Floris

  KEYWORDS: Nonlinear Oscillator, Random Dynamics, Gaussian White Noise, Joint Probability Density Function, Power Spectral Density

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.7 No.2, February 15, 2019

  ABSTRACT: A second order oscillator with nonlinear restoring force and nonlinear damping is considered: it is subject to both external and internal (parametric) excitations of Gaussian white noise type. The nonlinearities are chosen in such a way that the associated Fokker-Planck-Kolmogorov equation is solvable in the steady state. Different choices of some system parameters give rise to different and interesting shapes of the joint probability density function of the response, which in some cases appears to be multimodal. The problem of the determination of the power spectral density of the response is also addressed by using the true statistical linearization method.