Parametrically Excited Vibration of a Timoshenko Beam on Random Viscoelastic Foundation jected to a Harmonic Moving Load
- 295 Downloads
The vibration response of a Timoshenko beam supported by a viscoelastic foundation with randomly distributed parameters along the beam length and jected to a harmonic moving load, is studied. By means of the first-order two-dimensional regular perturbation method and employing appropriate Green's functions, the dynamic response of the beam consisting of the mean and variance of the deflection and of the bending moment are obtained analytically in integral forms. Results of a field measurement for a test track are utilized to model the uncertainty of the foundation parameters. A frequency analysis is carried out and the effect of the load speed on the response is studied. It is found that the covariance functions of the stiffness and the loss factor both have the shape of an exponential function multiplied by a cosine function. Furthermore, it is shown that in each frequency response there is a peak value for the frequency, which changes inversely with the load speed. It is also found that the peak value of the mean and also standard deviation of the deflection and bending moment can be a decreasing or increasing function of the load speed depending on its frequency.
KeywordsTimoshenko beam moving load parametrically excited vibration random viscoelastic foundation two-dimensional perturbation
Unable to display preview. Download preview PDF.
- 1.Fryba, L., Vibration of Solids and Structures Under Moving Loads, Thomas Telford, London, 1999.Google Scholar
- 4.Koh, C. G., Ong, J. S. Y, Chua, D. K. H., and Feng, J., ‘Moving element method for train-track dynamics’, International Journal for Numerical Methods in Engineering 56(11), 2003, 1549–1567.Google Scholar
- 5.Kim, S-M., ‘Stability and dynamic response of Rayleigh beam–columns on an elastic foundation under moving loads of constant amplitude and harmonic variation’, Engineering Structures 27(6), 2005, 869–880Google Scholar
- 7.Naprstk, J. and Fryba, L., ‘Interaction of a Long Beam on Stochastic Foundation With a Moving Random Load’, in Structural Dynamics: Recent Advances, The Institute of Sound and Vibration Research, Southampton, 1993.Google Scholar
- 8.Naprstk, J. and Fryba, L., ‘Stochastic modelling of track and its substructure In: interaction of railway vehicles with the track and its substructure’, Supplement to Vehicle System Dynamics 24, 1995, 297–310.Google Scholar
- 9.Andersen, L. and Nielsen, R. K., ‘Vehicle moving along a beam on a random modified Kelvin foundation’, in Proceeding of 8th International Congress on Sound and Vibration ICSV8, Hong Kong, 2001.Google Scholar
- 11.Oscarsson, J., ‘Dynamic train/track interaction – linear and non-linear track models with property scatter’, Ph.D Thesis, Department of Solid Mechanics, Chalmers University of Technology, Goteborg, 2001.Google Scholar
- 16.Kargarnovin, M. H. and Younesian, D., ‘Dynamic response analysis of Timoshenko beam on viscoelastic foundation under an arbitrary distributed harmonic moving load’, in Proceeding of the 5th International Conference on Structural Dynamics, EURODYN, Munich, 2002.Google Scholar
- 18.Nyfeh, A. H. and Mook, D., Nonlinear Oscillations, Wiley, New York, 1979.Google Scholar
- 22.Solnes, J., Stochastic Processes and Random Vibration, Wiley, New York, 1997.Google Scholar
- 23.George, R., ‘Railway ballast quality monitoring’, Technical report, Institute of Sound and Vibration Research, University of Southampton, 2003.Google Scholar