https://doi.org/10.1140/epjst/e2011-01383-5
Regular Article
Response of SDOF nonlinear oscillators with lightly fractional derivative damping under real noise excitations
1 College of Civil Engineering, Huaqiao University, Xiamen 361021, China
2 School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
3 Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China
a e-mail: wqzhu@yahoo.com
Received:
1
December
2010
Revised:
27
January
2011
Published online:
4
April
2011
This paper deals with the response of single-degree-of-freedom (SDOF) strongly nonlinear oscillator with lightly fractional derivative damping to external and (or) parametric real noise excitations. First, the state vector of the displacement and the velocity is approximated by one-dimensional time-homogeneous diffusive Markov process of amplitude through using the stochastic averaging method. Then, the stationary probability density of amplitude is obtained by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the averaged Itô equation of amplitude, in which the Fourier series expansions are used to obtain the explicit expressions of the drift and diffusion coefficients. Finally, the response of a Duffing oscillator with lightly fractional derivative damping under external and parametric real noise excitations is evaluated by using the proposed procedure and compared with that from the Monte Carlo simulation of original system.
© EDP Sciences, Springer-Verlag, 2011
