A Survey on Buckling and Vibrations of a Viscoelastic Beam under Distributed Lateral and Axial Loads
الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکحمید رضا ایپک چی 1 , حمیده صدیقی 2
1 - استادیار دانشکده مکانیک دانشگاه صنعتی شاهرود
2 - دانشجوی کارشناسی ارشد دانشکده مکانیک دانشگاه صنعتی شاهرود.
الکلمات المفتاحية: Viscoelastic beam vibration, Viscoelastic beam buckling, Eigenfunctions expansion method, Axial and lateral loadings,
ملخص المقالة :
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.
[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
