Stochastic jump and bifurcation of Duffing oscillator with fractional derivative damping under combined harmonic and white noise excitations

被引：110

作者：

Chen, Lincong ^{[2
]}

Zhu, Weiqiu ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Mech, State Key Lab Fluid Power Transmiss & Control, Hangzhou 310027, Peoples R China

[2] Huaqiao Univ, Coll Civil Engn, Xiamen 361021, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2011年 / 46卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Fractional derivative damping; Duffing oscillator; Stochastic jump; Bifurcation; Combined harmonic and white noise excitations; NARROW-BAND EXCITATION; STRONGLY NONLINEAR OSCILLATORS; CHAOTIC DYNAMICS; DAMPED SYSTEMS; EQUATION; VIBRATION;

D O I：

10.1016/j.ijnonlinmec.2011.07.002

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

The stochastic jump and bifurcation of Duffing oscillator with fractional derivative damping of order a (0 < alpha < 1) under combined harmonic and white noise excitations are studied. First, the system state is approximately represented by two-dimensional time-homogeneous diffusive Markov process of amplitude and phase difference using the stochastic averaging method. Then, the method of reduced Fokker-Plank-Kolmogorov (FPK) equation is used to predict the stationary response of the original system. The phenomenon of stochastic jump and bifurcation as the fractional orders' change is examined. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1324 / 1329

页数：6

共 30 条

[1]

Agrawal O P, 1999, P 1999 ASME DES ENG, P12

[2] Stochastic analysis of a 1-D system with fractional damping of order 1/2 [J].

Agrawal, OP .

JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 2002, 124 (03) :454-460

[3]

[Anonymous], 1993, INTRO FRACTIONAL CA

[4] NONLINEARLY DAMPED SYSTEMS UNDER SIMULTANEOUS BROAD-BAND AND HARMONIC EXCITATIONS [J].

CAI, GQ ;

LIN, YK .

NONLINEAR DYNAMICS, 1994, 6 (02) :163-177

[5] Chaotic dynamics of the fractionally damped van der Pol equation [J].

Chen, Juhn-Horng ;

Chen, Wei-Ching .

CHAOS SOLITONS & FRACTALS, 2008, 35 (01) :188-198

[6] Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations [J].

Chen, L. C. ;

Zhu, W. Q. .

NONLINEAR DYNAMICS, 2009, 56 (03) :231-241

[7] First passage failure of SDOF nonlinear oscillator with lightly fractional derivative damping under real noise excitations [J].

Chen, Lincong ;

Zhu, Weigiu .

PROBABILISTIC ENGINEERING MECHANICS, 2011, 26 (02) :208-214

[8] NUMERICAL SIMULATIONS OF JUMP PHENOMENA IN STABLE DUFFING SYSTEMS [J].

FANG, T ;

DOWELL, EH .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 1987, 22 (03) :267-274

[9] Statistical analysis for stochastic systems including fractional derivatives [J].

Huang, Z. L. ;

Jin, X. L. ;

Lim, C. W. ;

Wang, Y. .

NONLINEAR DYNAMICS, 2010, 59 (1-2) :339-349

[10] Response and stability of a SDOF strongly nonlinear stochastic system with light damping modeled by a fractional derivative [J].

Huang, Z. L. ;

Jin, X. L. .

JOURNAL OF SOUND AND VIBRATION, 2009, 319 (3-5) :1121-1135

← 1 2 3 →