Iteration method for equation of viscoelastic motion with fractional differential operator of damping

被引：38

作者：

Ingman, D ^{[1
]}

Suzdalnitsky, J ^{[1
]}

机构：

[1] Technion Israel Inst Technol, QAR, IL-32000 Haifa, Israel

来源：

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2001年 / 190卷 / 37-38期

关键词：

fractional derivative; numerical methods; viscoelastic;

D O I：

10.1016/S0045-7825(00)00361-3

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Mechanical properties of viscoelastic materials depend on the loading conditions and their history. The work is devoted to the analysis of oscillation processes in viscoelastic media, with loading prehistory taken into account by means of fractional derivative terms in the governing equations. The paper suggests convergent procedure for numerical solution of this type of differential equations and their system for any combination of damping operator orders. The order of the fractional derivative may be as constant, so variable. Analysis of the amplitude-frequency behavior of the oscillator versus the damping operator order is provided. (C) 2001 Elsevier Science B.V. All rights reserved.

引用

页码：5027 / 5036

页数：10

共 17 条

[1]

[Anonymous], 1974, Elementary Functional Analysis

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

BAGLEY, RL ;

TORVIK, PJ .

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

[3] FRACTIONAL ORDER STATE-EQUATIONS FOR THE CONTROL OF VISCOELASTICALLY DAMPED STRUCTURES [J].

BAGLEY, RL ;

CALICO, RA .

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 1991, 14 (02) :304-311

[4] ON THE FRACTIONAL CALCULUS MODEL OF VISCOELASTIC BEHAVIOR [J].

BAGLEY, RL ;

TORVIK, PJ .

JOURNAL OF RHEOLOGY, 1986, 30 (01) :133-155

[5]

Bagley RL, 1979, SHOCK VIBRATION B 2, V49, P135

[6] Fractional integral formulation of constitutive equations of viscoelasticity [J].

Enelund, M ;

Fenander, A ;

Olsson, P .

AIAA JOURNAL, 1997, 35 (08) :1356-1362

[7] Time-domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations [J].

Enelund, M ;

Josefson, BL .

AIAA JOURNAL, 1997, 35 (10) :1630-1637

[8] Modal synthesis when modeling damping by use of fractional derivatives [J].

Fenander, A .

AIAA JOURNAL, 1996, 34 (05) :1051-1058

[9]

GLOCKLE WG, 1991, MACROMOLECULES, V24, P6426

[10]

INGMAN D, 1998, EEP, V25, P199

← 1 2 →