A Survey on Buckling and Vibrations of a Viscoelastic Beam under Distributed Lateral and Axial Loads

Document Type: Persian

Authors

1 Assistant Professor, Mechanical Engineering Faculty, Shahrood University of Technology

2 M.Sc. Student, Mechanical Engineering Faculty, Shahrood University of Technology

Abstract

In this paper, based on Kelvin and Linear Standard Solid models, dynamic response and the buckling load of a viscoelastic beam under  lateral and axial loads have been determined. The governing equations have been extracted using Euler  and Timoshenko theories and their analytical solutions have been obtained by using the eigenfunctions expansion method. Buckling load have been calculated by using the Euler and Timoshenko beam theories based on Kelvin and standard models. The results have been compared with the elastic case. The results show that the simulation of a viscoelastic beam with an elastic case, is not a reasonable approximation for moderately high damping. Also, the damping parameter has not been  appeared explicitly in the buckling load determination, even though the buckling load of a viscoelastic beam is 50% more than an elastic beam.   

Keywords


[1] Timoshenko S.P, Gere J.M, Theory of Elastic

Stability, Mc Graw-Hill Company, 1985.

[2] Mirsky I .,Hermann G., Axially Symmetric

Motion of Thick Cylindrical Shells, Journal of

Applied Mechanics, 1958, 25, pp. 99-152.

[3] Baber T.T., Maddox R. A., Orozco C.E., A

finite element model for harmonically excited

viscoelastic sandwich beams, Computers &

Structures, 66 (1), 1998, pp. 105-113.

[4] Branca F., Guillermo J. , Nonlinear viscoelastic

analysis of thin-walled beams in composite

material, Thin-Walled Structures , 41, 2003, pp.

957-971 .

[5] Ganesan N., Pradeep V., Buckling and vibration

of sandwich beam with viscoelastic core under

thermal environments, Journal of Sound and

Vibration, 286 (4-5), 2005, pp. 1067-1074.

[6] Kocatürk T., Şimşek M., Dynamic analysis of

eccentrically prestressed viscoelastic

Timoshenko beam under a moving harmonic

load, Computers & Structures, 84(31-32) ,

2006, pp. 2113-2127.

 [7] Salehi M., Ansari F., Viscoelastic buckling of

Euler-Bernoulli and Timoshenko beams under

time variant general loading condition, Iranian

Polymer Journal ,15(3), 2006, pp.183-193.

[8] Seong M., Yoon H., Vibration and dynamic

buckling of shear beam-columns on elastic

foundation under moving harmonic loads,

International Journal of Solids and Structures,

43, 2006, pp. 393–412.

[9] Mahmoudi S.N, Khadem S., Kokabi M., Nonlinear

free vibrations of Kelvin–Voigt viscoelastic

beams, International Journal of

Mechanical Sciences, 49, 2007, pp. 722–732.

[10] Ganesan S.N., Sethuraman R., Buckling and

free vibration analysis of magnetic constrained

layer damping (MCLD) beam, Finite Elements

in Analysis and Design, 45, 2009, pp. 156-162.

[11] Kiani K., Nikkhoo A., Mehri B., Parametric

analyses of multispan viscoelastic shear

deformable beams under excitation of a moving

mass, Journal of Vibration and Acoustics, 131,

2009, pp. 1-12.

[12] Mofid M. , Tehranchi A., Ostadhossein A., On

the viscoelastic beam subjected to moving mass,

Advances in Engineering Software, 41(2), 2010,

pp. 240-247.

[13] Arvin H., Sadighi M., Ohadi A.R., A

numerical study of free and forced vibration of

composite sandwich beam with viscoelastic

core, Composite Structures, 92(4), 2010, pp.

996-1008.

[14] Hagadon P. , Dasgupa A. ,Vibration and

Waves in Continuous Mechanical System, John

Wiley Company, 2007.

[15] Drozdov A., Viscoelastic Structures, Academic