Mathematical Analysis of Shearing Viscoelastic Beam Subjected to Continuous Moving Load

Document Type: Persian

Authors

1 M.Sc. Graduated, Shahrood University of Technology

2 Assistant Professor, Shahrood University of Technology

Abstract

In this paper, the dynamic response of a viscoelastic beam subjected to a moving distributed load has been studied. The viscoelastic properties of the beam have been considered as linear standard model in shear and incompressible in bulk. The stress components have been separated to the shear and dilatation components and as a result the governing equations in viscoelastic form has been obtained using direct method. These equations have been solved by the eigenfunction expansion method. In this research, according to the introduced dimensionless coefficients, a parametric study has been presented and the effects of the load velocity and viscoelastic materials have been investigated. The obtained results show the maximum decay corresponds to the cases that the first natural period equals totimes that the relaxation time.

Keywords


[1] HUANG C. C., Forced motions of viscoelastic cylindrical, Journal of Sound and Vibration,39(3), 1975, pp. 273-286.

[2] HUANG C. C., Forced motions of viscoelastic thick cylindrical shell, Journal of Sound and Vibration, 45(4), 1976, pp. 529-537.

[3] HUANG C. C., Moving loads on viscoelastic cylindrical shells, Journal of Sound and Vibration, 60(3), 1978, pp. 351-358.

[4] Fung R.F., Hang J.  and Echen W., Dynamic stability of a viscoelastic beam subjected to harmonic and parametric excitations simultaneously, Journal of Sound and Vibration, 198, 1996, pp. 1–16.

[5] Karnaukhov V. G., Kirichok I. F., Vibrations and dissipative heating of a viscoelastic beam under a moving load ,  Journal of Sound and Vibration ,41(1), 2005, pp. 49 – 55.

[6] Kocatürk T., Şimşek M., Vibration of viscoelastic beams subjected to an eccentric compressive force and a concentrated moving harmonic force, Journal of Sound and Vibration, 291, 2006, pp. 302–322,

[7] Kocatürk T., Şimşek M., Dynamic analysis of eccentrically prestressed viscoelastic Timoshenko beams under a moving harmonic load , Computers and Structures , 84, 2006, pp. 2113–2127.

[8] Şimşek M., Kocatürk T., Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load, Journal of Sound and Vibration, 320, 2009, pp. 235–253.

[9] Mofid M., Tehranchi A., Ostadhossein A., On the viscoelastic beam subjected to moving mass, Advances in Engineering Software, 41, 2010, pp. 240-243.

[10] Fryba L., Vibration of solids and structures under moving loads., The Netherlands Noordhoff International, 1972.

[11] Riande E., Calleja R.D., Prolongo M.G., Masegosa R.M., Salom C., Polymer viscoelasticity stress and strain in practice, Marcel Dekker INC, 2000.