Nonstationary Probability Densities of System Response of Strongly Nonlinear Single-Degree-of-Freedom System Subject to Modulated White Noise Excitation

JIN Xiao-ling; HUANG Zhi-long; LEUNG Andrew Y T

doi:10.3879/j.issn.1000-0887.2011.11.004

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JIN Xiao-ling, HUANG Zhi-long, LEUNG Andrew Y T. Nonstationary Probability Densities of System Response of Strongly Nonlinear Single-Degree-of-Freedom System Subject to Modulated White Noise Excitation[J]. Applied Mathematics and Mechanics, 2011, 32(11): 1294-1305. doi: 10.3879/j.issn.1000-0887.2011.11.004

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Nonstationary Probability Densities of System Response of Strongly Nonlinear Single-Degree-of-Freedom System Subject to Modulated White Noise Excitation

doi: 10.3879/j.issn.1000-0887.2011.11.004

1.
Department of Mechanics, Zhejiang University, Hangzhou 310027, P. R. China;

Received Date: 2010-09-10
Rev Recd Date: 2011-09-05
Publish Date: 2011-11-15

Abstract

Abstract

The nonstationary probability densities of system response of a single-degree-of-freedom system with lightly nonlinear damping and strongly nonlinear stiffness subject to dulated white noise excitation were studied.Using the stochastic averaging method based on the generalized harmonic functions,the averaged Fokker-Planck-Kolmogorov equation governing the nonstationary probability density of the amplitude was derived.The solution of the equation was approximated by a series expansion in terms of a set of properly selected basis functions with time-dependent coefficients.According to the Galerkin method,the time-dependent coefficients can be solved from a set of first-order linear differential equations.Then the semi-analytical formulae of the nonstationary probability density of the amplitude response as well as the nonstationary probability density of the state response and the statistic moments of the amplitude response can be obtained.A van der Pol-Duffing oscillator subject to modulated white noise was given as an example to illustrate the proposed procedures.The effects of the system parameters,such as linear damping coefficient and nonlinear stiffness coefficient,on the system response were discussed.
- nonstationary probability density,
- modulated white noise,
- stochastic averaging method,
- Galerkin method

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References(26)

References

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