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

[11]

KHASMINSKII RZ, 1968, KIBERNETKA, V3, P260

[12] APPLICATION OF FRACTIONAL DERIVATIVES TO SEISMIC ANALYSIS OF BASE-ISOLATED MODELS [J].

KOH, CG ;

KELLY, JM .

EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, 1990, 19 (02) :229-241

[13] Dynamical stability of viscoelastic column with fractional derivative constitutive relation [J].

Li, GG ;

Zhu, ZY ;

Cheng, CJ .

APPLIED MATHEMATICS AND MECHANICS-ENGLISH EDITION, 2001, 22 (03) :294-303

[14] SPRING VISCOUS DAMPER SYSTEMS FOR COMBINED SEISMIC AND VIBRATION ISOLATION [J].

MAKRIS, N ;

CONSTANTINOU, MC .

EARTHQUAKE ENGINEERING & STRUCTURAL DYNAMICS, 1992, 21 (08) :649-664

[15]

Oldham K.B., 1974, The fractional calculus theory and applications of differentiation and integration to arbitrary order, DOI DOI 10.1016/S0076-5392(09)60219-8

[16] Nonlinear vibrations of fractionally damped systems [J].

Padovan, J ;

Sawicki, JT .

NONLINEAR DYNAMICS, 1998, 16 (04) :321-336

[17] Visco-hyperelastic model for filled rubbers used in vibration isolation [J].

Papoulia, KD ;

Kelly, JM .

JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY-TRANSACTIONS OF THE ASME, 1997, 119 (03) :292-297

[18] Analysis of four-parameter fractional derivative model of real solid materials [J].

Pritz, T .

JOURNAL OF SOUND AND VIBRATION, 1996, 195 (01) :103-115

[19]

Rossikhin Y. A., 1997, Applied Mechanics Reviews, V50, P15, DOI [10.1115/1.3101682, DOI 10.1115/1.3101682]

[20] Analysis of free non-linear vibrations of a viscoelastic plate under the conditions of different internal resonances [J].

Rossikhin, YA ;

Shitikova, MV .

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2006, 41 (02) :313-325

← 1 2 3 4 →