### The influence of foundation mass on dynamic response of track-vehicle interaction

#### Abstract

The influence of foundation mass on the dynamic response of track-vehicle interaction is studied in this paper. The moving vehicle is modeled as a two-axle mass-spring-damper four-degrees-of-freedom system. A new dynamic foundation model, called "Dynamic foundation model" including linear elastic spring, shear layer, viscous damping and foundation mass parameter, is used to analyze the dynamic response of the track-vehicle interaction. The railway track on the new dynamic foundation model subjected to a moving vehicle is regarded as an integrated system. By means of the finite element method and dynamic balance principle, the governing equation of motion for railway track-vehicle-foundation interaction is derived and solved by the step-by-step integration method. The accuracy of the algorithm is verified by comparing the numerical results with the other numerical results in the literature. The influence of foundation mass parameter on the dynamic response of railway track-vehicle interaction is investigated. The numerical results show that with the new dynamic foundation model the foundation mass effects more significantly on the dynamic response of track-vehicle interaction. The study shows that the new dynamic foundation model describes the true behavior of soil in the analysis of dynamic response of structures on the foundation.

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E. Winckler. Die lehre von elastizitat und festigkeit. Dominicus, Prague, (1867).

D. Younesian, Z. Saadatnia, and H. Askari. Analytical solutions for free oscillations of beams on nonlinear elastic foundations using the variational iteration method. Journal of Theoretical and Applied Mechanics, 50, (2), (2012), pp. 639–652.

R. U. A. Uzzal, R. B. Bhat, and W. Ahmed. Dynamic response of a beam subjected to moving load and moving mass supported by Pasternak foundation. Shock and Vibration, 19, (2), (2012), pp. 205–220. doi:10.1155/2012/919512.

K. Q. Do and T. C. Nguyen. Dynamic response of plate on visco-elastic foundation considering the mass of moving object. In International Symposium on Dynamics and Control, Hanoi, (2012), pp. 215–227.

J. S. Kim and M. K. Kim. The dynamic response of an Euler-Bernoulli beam on an elastic foundation by finite element analysis using the exact stiffness matrix. Journal of Physics: Conference Series, 382, (1), (2012). doi:10.1088/1742-6596/382/1/012008.

D. K. Nguyen, T. H. Trinh, and G. B. Sthenly. Post-buckling response of elastic-plastic beam resting on an elastic foundation to eccentric axial load. The IES Journal Part A: Civil & Structural Engineering, 5, (1), (2012), pp. 43–49. doi:10.1080/19373260.2012.652769.

L. Wang, J. Ma, J. Peng, and L. Li. Large amplitude vibration and parametric instability of inextensional beams on the elastic foundation. International Journal of Mechanical Sciences, 67, (2013), pp. 1–9. doi:10.1016/j.ijmecsci.2012.12.002.

S. B. Coşkun, B. Öztürk, and U. Mutman. Adomian decomposition method for vibration of nonuniform Euler beams on elastic foundation. In Proceedings of the 9th International Conference on Structural Dynamics, EURODYN 2014, Porto, Portugal, (2014), pp. 1935–1940.

P. C. Jorge, F. M. F. Simões, and A. P. Da Costa. Dynamics of beams on non-uniform nonlinear foundations subjected to moving loads. Computers & Structures, 148, (2015), pp. 26–34. doi:10.1016/j.compstruc.2014.11.002.

D. Froio, R. G. Moioli, and E. Rizzi. Numerical dynamic analysis of beams on nonlinear elastic foundations under harmonic moving load. Eccomas Proceedia, 2149, (2016), pp. 4784–4809. doi:10.7712/100016.2149.7515.

I. B. Teodoru. Beams on elastic foundation the simplified continuum approach. Buletinul Institutului Politehnic din lasi. Sectia Constructii, Arhitectura, 55, (4), (2009), pp. 37–45.

M. M. Filonenko-Borodich. Some approximate theories of elastic foundation. Uchenyie Zapiski Moskovkogo Gosudarstuennogo Universiteta Mekhanika, Moscow, 46, (1940), pp. 3–18. (in Russian).

M. Hetényi. Beams on elastic foundation: theory with applications in the fields of civil and mechanical engineering. University of Michigan Press, Ann Arbor, (1946).

M. Hetényi. Beams on elastic foundation. University of Michigan Press, (1950).

P. L. Pasternak. On a new method of analysis of an elastic foundation by means of two constants. Gosudarstvennoe Izdatelstvo Literaturi po Stroitelstvui Arkhitekture, (1954). (in Russian).

E. Reissner. A note on deflections of plates on a viscoelastic foundation. Journal of Applied Mechanics, 25, (1958), pp. 144–145.

E. Reissner. Note on the formulation of the problem of the plate on an elastic foundation. Acta Mechanica, 4, (1), (1967), pp. 88–91. doi:10.1007/bf01291090.

A. D. Kerr. Elastic and viscoelastic foundation models. Journal of Applied Mechanics, 31, (3), (1964), pp. 491–498. doi:10.1115/1.3629667.

A. D. Kerr. A study of a new foundation model. Acta Mechanica, 1, (2), (1965), pp. 135–147. doi:10.1007/bf01174308.

V. Z. Vlasov and U. N. Leont’ev. Beams, plates and shells on elastic foundation. Israel Program for Scientific Translation, (1966).

R. Jones and J. Xenophontos. The Vlasov foundation model. International Journal of Mechanical Sciences, 19, (6), (1977), pp. 317–323. doi:10.1016/0020-7403(77)90084-4.

K. Ozgan. Dynamic analysis of thick plates including deep beams on elastic foundations using modified Vlasov model. Shock and Vibration, 20, (1), (2013), pp. 29–41. doi:10.1155/2013/856101.

D. T. Pham, P. H. Hoang, and T. P. Nguyen. Dynamic response of beam on a new foundation model subjected to a moving oscillator by finite element method. In 16th Asia Pacific Vibration Conference, Hanoi, Vietnam, (2015), pp. 244–250.

T. P. Nguyen, D. T. Pham, and P. H. Hoang. A new foundation model for dynamic analysis of beams on nonlinear foundation subjected to a moving mass. Procedia Engineering, 142, (2016), pp. 166–173. doi:10.1016/j.proeng.2016.02.028.

P. T. Nguyen, T. D. Pham, and H. P. Hoang. A dynamic foundation model for the analysis of plates on foundation to a moving oscillator. Structural Engineering and Mechanics, 59, (6), (2016), pp. 1019–1035. doi:10.12989/sem.2016.59.6.1019.

D. T. Pham, P. H. Hoang, and T. P. Nguyen. Dynamic response of beam on a new non-uniform dynamic foundation subjected to a moving vehicle using finite element method. IJERT, 6, (3), (2017), pp. 279–285. doi:10.17577/ijertv6is030244.

T. D. Pham, P. H. Hoang, and T. P. Nguyen. Experiments on influence of foundation mass on dynamic characteristic of structures. Structural Engineering and Mechanics, 65, (5), (2018), pp. 505–511.

P. Lou. A vehicle-track-bridge interaction element considering vehicle’s pitching effect. Finite Elements in Analysis and Design, 41, (4), (2005), pp. 397–427. doi:10.1016/j.finel.2004.07.004.

S. H. Ju. Finite element investigation of traffic induced vibrations. Journal of Sound and Vibration, 321, (3-5), (2009), pp. 837–853. doi:10.1016/j.jsv.2008.10.031.

T. Yokoyama. Vibration analysis of Timoshenko beam-columns on two-parameter elastic foundations. Computers & Structures, 61, (6), (1996), pp. 995–1007. doi:10.1016/0045-7949(96)00107-1.

H. Matsunaga. Vibration and buckling of deep beam-columns on two-parameter elastic foundations. Journal of Sound and Vibration, 228, (2), (1999), pp. 359–376. doi:10.1006/jsvi.1999.2415.

H. Ding, K. L. Shi, L. Q. Chen, and S. P. Yang. Dynamic response of an infinite Timoshenko beam on a nonlinear viscoelastic foundation to a moving load. Nonlinear Dynamics, 73, (1-2), (2013), pp. 285–298. doi:10.1007/s11071-013-0784-0.

DOI: https://doi.org/10.15625/0866-7136/12255

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