Wave equation for generalized Zener model containing complex order fractional derivatives

被引：11

作者：

Atanackovic, Teodor M. ^{[1
]}

Janev, Marko ^{[2
]}

Konjik, Sanja ^{[3
]}

Pilipovic, Stevan ^{[3
]}

机构：

[1] Univ Novi Sad, Inst Mech, Fac Tech Sci, Trg D Obradovica 6, Novi Sad 21000, Serbia

[2] Serbian Acad Arts & Sci, Inst Math, Kneza Mihaila 36, Belgrade 11000, Serbia

[3] Univ Novi Sad, Dept Math & Informat, Fac Sci, Trg D Obradovica 4, Novi Sad 21000, Serbia

来源：

CONTINUUM MECHANICS AND THERMODYNAMICS | 2017年 / 29卷 / 02期

关键词：

Fractional derivative of complex order; Constitutive equation; Thermodynamical restriction; Wave propagation;

D O I：

10.1007/s00161-016-0548-4

中图分类号：

O414.1 [热力学];

学科分类号：

摘要：

We study waves in a viscoelastic rod whose constitutive equation is of generalized Zener type that contains fractional derivatives of complex order. The restrictions following from the Second Law of Thermodynamics are derived. The initial boundary value problem for such materials is formulated and solution is presented in the form of convolution. Two specific examples are analyzed.

引用

页码：569 / 583

页数：15

共 24 条

[1]

Amendola G, 2012, THERMODYNAMICS OF MATERIALS WITH MEMORY: THEORY AND APPLICATIONS, P1, DOI 10.1007/978-1-4614-1692-0

[2]

Atanackovic T.M., 2014, Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes

[3] Complex order fractional derivatives in viscoelasticity [J].

Atanackovic, Teodor M. ;

Konjik, Sanja ;

Pilipovic, Stevan ;

Zorica, Dusan .

MECHANICS OF TIME-DEPENDENT MATERIALS, 2016, 20 (02) :175-195

[4] Vibrations of an elastic rod on a viscoelastic foundation of complex fractional Kelvin-Voigt type [J].

Atanackovic, Teodor M. ;

Janev, Marko ;

Konjik, Sanja ;

Pilipovic, Stevan ;

Zorica, Dusan .

MECCANICA, 2015, 50 (07) :1679-1692

[5] Thermodynamical Restrictions and Wave Propagation for a Class of Fractional Order Viscoelastic Rods [J].

Atanackovic, Teodor M. ;

Konjik, Sanja ;

Oparnica, Ljubica ;

Zorica, Dusan .

ABSTRACT AND APPLIED ANALYSIS, 2011,

[6] Distributed-order fractional wave equation on a finite domain: creep and forced oscillations of a rod [J].

Atanackovic, Teodor M. ;

Pilipovic, Stevan ;

Zorica, Dusan .

CONTINUUM MECHANICS AND THERMODYNAMICS, 2011, 23 (04) :305-318

[7] A modified Zener model of a viscoelastic body [J].

Atanackovic, TM .

CONTINUUM MECHANICS AND THERMODYNAMICS, 2002, 14 (02) :137-148

[8] Distributed-order fractional wave equation on a finite domain. Stress relaxation in a rod [J].

Atanackovica, T. M. ;

Pilipovic, S. ;

Zorica, D. .

INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE, 2011, 49 (02) :175-190

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

BAGLEY, RL ;

TORVIK, PJ .

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

[10]

DOETSCH G, 1950, HDB LAPLACE TRANSFOR, V1

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