Stochastic averaging of strongly nonlinear oscillators with small fractional derivative damping under combined harmonic and white noise excitations

被引：58

作者：

Chen, L. C. ^{[1
]}

Zhu, W. Q. ^{[1
]}

机构：

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

来源：

NONLINEAR DYNAMICS | 2009年 / 56卷 / 03期

基金：

中国国家自然科学基金;

关键词：

Stochastic averaging method; Fractional derivative damping; Strongly nonlinear oscillator; Combined harmonic and white noise excitations; First passage failure; VISCOELASTICALLY DAMPED STRUCTURES; VIBRATION ISOLATION; CHAOTIC DYNAMICS; CALCULUS; SYSTEMS; EQUATION; MODEL;

D O I：

10.1007/s11071-008-9395-6

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

A stochastic averaging method for strongly nonlinear oscillators with lightly fractional derivative damping of order alpha (0 <alpha < 1) under combined harmonic and white noise external and (or) parametric excitations is proposed and then applied to study the first passage failure of Duffing oscillator with lightly fractional derivative damping of order 1/2 under combined harmonic and white noise excitations in the case of primary parametric resonance. Numerical results show that the proposed method works very well.

引用

页码：231 / 241

页数：11

共 37 条

[1]

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

[2] Analytical solution for stochastic response of a fractionally damped beam [J].

Agrawal, OP .

JOURNAL OF VIBRATION AND ACOUSTICS-TRANSACTIONS OF THE ASME, 2004, 126 (04) :561-566

[3] 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

[4]

[Anonymous], 1993, INTRO FRACTIONAL CA

[5] FRACTIONAL CALCULUS IN THE TRANSIENT ANALYSIS OF VISCOELASTICALLY DAMPED STRUCTURES [J].

BAGLEY, RL ;

TORVIK, PJ .

AIAA JOURNAL, 1985, 23 (06) :918-925

[6] FRACTIONAL CALCULUS - A DIFFERENT APPROACH TO THE ANALYSIS OF VISCOELASTICALLY DAMPED STRUCTURES [J].

BAGLEY, RL ;

TORVIK, PJ .

AIAA JOURNAL, 1983, 21 (05) :741-748

[7] A THEORETICAL BASIS FOR THE APPLICATION OF FRACTIONAL CALCULUS TO VISCOELASTICITY [J].

BAGLEY, RL ;

TORVIK, PJ .

JOURNAL OF RHEOLOGY, 1983, 27 (03) :201-210

[8] 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

[9]

GAUL L, 1989, MECH RES COMMUN, V16, P4447

[10] Fractional calculus via functional calculus:: Theory and applications [J].

Kempfle, S ;

Schäfer, I ;

Beyer, H .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :99-127

← 1 2 3 4 →