Vibrations of an elastic rod on a viscoelastic foundation of complex fractional Kelvin-Voigt type

被引：23

作者：

Atanackovic, Teodor M. ^{[1
]}

Janev, Marko ^{[2
]}

Konjik, Sanja ^{[3
]}

Pilipovic, Stevan ^{[3
]}

Zorica, Dusan ^{[2
]}

机构：

[1] Univ Novi Sad, Dept Mech, Fac Tech Sci, Novi Sad 21000, Serbia

[2] Serbian Acad Arts & Sci, Math Inst, Beograd 11000, Serbia

[3] Univ Novi Sad, Dept Math, Fac Sci, Novi Sad 21000, Serbia

来源：

MECCANICA | 2015年 / 50卷 / 07期

关键词：

Transversal vibrations; Dynamic stability; Elastic rod on viscoelastic foundation; Fractional order constitutive equations; Real andcomplex order fractional derivatives; DYNAMIC STABILITY; COLUMN;

D O I：

10.1007/s11012-015-0128-x

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

We consider vibrations of an elastic rod loaded by axial force of constant intensity and positioned on a viscoelastic foundation of complex order fractional derivative type. The solution to the problem is obtained by the separation of variables method. The critical value of axial force, guaranteeing stability, is determined.

引用

页码：1679 / 1692

页数：14

共 25 条

[1] Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory [J].

Aranda-Ruiz, J. ;

Loya, J. ;

Fernandez-Saez, J. .

COMPOSITE STRUCTURES, 2012, 94 (09) :2990-3001

[2]

Atanackovic T., 1997, Stability theory of elastic rods

[3]

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

[4] Expansion formula for fractional derivatives in variational problems [J].

Atanackovic, Teodor M. ;

Janev, Marko ;

Konjik, Sanja ;

Pilipovic, Stevan ;

Zorica, Dusan .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 409 (02) :911-924

[5] Stability of an elastic rod on a fractional derivative type of foundation [J].

Atanackovic, TM ;

Stankovic, B .

JOURNAL OF SOUND AND VIBRATION, 2004, 277 (1-2) :149-161

[6]

Atanackovic TM, 2014, ARXIV14078294V1

[7]

Baclic BS, 2000, B ACAD SERB SCI ARTS, V121, P115

[8]

Chen W. F., 1976, THEORY BEAM COLUMNS, V1

[9] Stochastic stability of a fractional viscoelastic column under bounded noise excitation [J].

Deng, J. ;

Xie, W. -C. ;

Pandey, M. D. .

JOURNAL OF SOUND AND VIBRATION, 2014, 333 (06) :1629-1643

[10] A discrete mechanical model of fractional hereditary materials [J].

Di Paola, Mario ;

Pinnola, Francesco Paolo ;

Zingales, Massimiliano .

MECCANICA, 2013, 48 (07) :1573-1586

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