Some solutions of the nonhomogeneous Bagley-Torvik equation

被引：1

作者：

Aleroev, Temirkhan S. ^{[1
]}

Erokhin, Sergey ^{[1
]}

机构：

[1] Moscow State Univ Civil Engn, Appl Math Dept, 26 Yaroslayskoe Shosse, Moscow 129337, Russia

来源：

INTERNATIONAL JOURNAL OF MODELING SIMULATION AND SCIENTIFIC COMPUTING | 2019年 / 10卷 / 01期

关键词：

Fractional derivative; Bagley-Torvik equation; viscoelasticity; Laplace transform; FRACTIONAL CALCULUS;

D O I：

10.1142/S1793962319410022

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this study, nonhomogeneous differential equation of the second order is considered, which contains fractional derivative (Bagley-Torvik equation), where the derivative order ranges within 1 and 2. This equation is applied in mechanics of oscillation processes. To study the equation, we use the Laplace transform, which allows us to obtain an image of the solution in an explicit form. Two typical kinds of functions of the right-hand side of the equation are considered. Numerical solutions are constructed for each of them. The solutions obtained are compared with experimental information on polymer concrete samples. The comparison allows for the conclusion about the adequacy of the numerical and analytical solutions to the nonhomogeneous Bagley-Torvik equation.

引用

页数：6

共 11 条

[1]

Aleroev T, 2018, MATEM MODELIROVANIE, V30, P93

[2] Modeling of deformation-strength characteristics of polymer concrete using fractional calculus [J].

Aleroev, Temirkhan ;

Erokhin, Sergey ;

Kekharsaeva, Elmira .

XXI INTERNATIONAL SCIENTIFIC CONFERENCE ON ADVANCED IN CIVIL ENGINEERING CONSTRUCTION - THE FORMATION OF LIVING ENVIRONMENT (FORM 2018), 2018, 365

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

BAGLEY, RL ;

TORVIK, PJ .

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

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

BAGLEY, RL ;

TORVIK, PJ .

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

[5]

Draganescu GE, 2005, J OPTOELECTRON ADV M, V7, P877

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

Fenander, A .

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

[7] Existence for boundary value problems of two-term Caputo fractional differential equations [J].

Ibrahim, Badawi Hamza Elbadawi ;

Dong, Qixiang ;

Fan, Zhenbin .

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2017, 10 (02) :511-520

[8] Control of damping oscillations by fractional differential operator with time-dependent order [J].

Ingman, D ;

Suzdalnitsky, J .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2004, 193 (52) :5585-5595

[9]

Ingman D, 1983, COMPUT METH APPL MEC, V190, P5027

[10]

Kekharsaeva E, 2016, SBORN T 6 VSER NAUCH, P104

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