The probabilistic solutions of the nonlinear stochastic oscillators with even nonlinearity in displacement are investigated with the exponential-polynomial closure method. Numerical results show that the results obtained from the exponential-polynomial closure method agree well with the simulated solution in the presented case, even if the mean of displacement is nonzero and the probability density function of the displacement is nonsymmetric about its mean.

References

References
1.
Booton
,
R. C.
, 1954, “
Nonlinear Control Systems with Random Inputs
,”
IRE Trans. Circuit Theory
,
CT-1
(
1
), pp.
9
18
.
2.
Lin
,
Y. K.
, and
Cai
,
G. Q.
, 1995,
Probabilistic Structural Dynamics
,
McGraw-Hill, International Editions
,
New York
.
3.
Socha
,
L.
, 2008,
Linearization Methods for Stochastic Dynamic Systems
,
Springer-Verlag
,
Berlin
.
4.
Harris
,
C. J.
, 1979, “
Simulation of Multivariate Nonlinear Stochastic System
,”
Int. J. for Numer. Mech. Eng.
,
14
, pp.
37
50
.
5.
Kloeden
,
P. E.
, and
Platen
,
E.
, 1995,
Numerical Solution of Stochastic Differential Equations
,
Springer-Verlag
,
Berlin
.
6.
Er
,
G. K.
, 1998, “
A New Non-Gaussian Closure Method for the PDF Solution of Nonlinear Random Vibrations, Engineering Mechanics: A Force for the 21st Century
,”
ASCE 12th Engineering Mechanics Conference
,
H.
Murakami
,
J. E.
Luco
, eds., Reston, pp.
1400
1406
.
7.
Er
,
G. K.
, 1998, “
An Improved Non-Gaussian Closure Method for Randomly Excited Nonlinear Stochastic Systems
,”
Nonlinear Dyn.
,
17
(
3
), pp.
285
297
.
8.
Er
,
G. K.
, 2000, “
The Probabilistic Solution to Non-Linear Random Vibrations of Multi-Degree-of-Freedom Systems
,”
ASME J. Appl. Mech.
,
67
, pp.
355
359
.
9.
Er
,
G. K.
, 2011, “
Methodology for the Solutions of Some Reduced Fokker-Planck Equations in High Dimensions
,”
Ann. Phys.
,
523
(
3
), pp.
247
258
.
10.
Er
,
G. K.
, and
Iu
,
V. P.
, 2011, “
A New Method for the Probabilistic Solutions of Large-Scale Nonlinear Stochastic Dynamic Systems
,”
Nonlinear Stochastic Dynamics and Control
,
W. Q.
Zhu
,
Y. K.
Lin
, and
G. Q.
Cai
, eds.,
Springer
,
Berlin
, pp.
25
34
.
11.
Chaudhary
,
A. K.
,
Bhatia
,
V. B.
,
Das
,
M. K.
, and
Tavakol
,
R. K.
, 1995, “
Statistical Response of Randomly Excited Nonlinear Radial Oscillations in Polytropes
,”
J. Astrophys. Astron.
,
16
, pp.
45
52
.
You do not currently have access to this content.