Research Articles | Challenge Journal of Structural Mechanics

The assessment of soil depth sensitivity to dynamic behavior of the Euler-Bernoulli beam under accelerated moving load

Amin Ghannadiasl, Hasan Rezaei Dolagh



Dynamic behavior is one of the most crucial characters in the railways structures. One of the items which leads to precise identification of the dynamic behavior of railways is the soil depth beneath them. In this paper, an Euler-Bernoulli beam on a finite depth foundation under accelerated moving load is presented. The dynamic equilibrium in the vertical direction is only regarded in accordance with the factor of finite beams. In this study, the dynamic equilibrium of the soil in the vertical direction and the sensitivity of soil depth are considered. The governing equations are simulated by using Fourier transform method. Eventually, by considering the sequences of shear waves, and different kinds of damping, displacement of the beam is obtained for the various acceleration, times and soil depth. As a result, it is shown that, higher acceleration is not dramatically effective on the beam displacement. Also, foundation inertia causes a significant reduction in critical velocity and can augment the beam response.


Euler-Bernoulli beam; accelerated moving load; soil depth; railway structure

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Abu-Hilal M (2003). Forced vibration of Euler–Bernoulli beams by means of dynamic Green functions. Journal of sound and vibration, 267(2), 191-207.

Balkaya M, Kaya MO, Sağlamer A (2009). Analysis of the vibration of an elastic beam supported on elastic soil using the differential transform method. Archive of Applied Mechanics, 79(2), 135-146.

Barari A, Kaliji HD, Ghadimi M, Domairry G (2011). Non-linear vibration of Euler-Bernoulli beams. Latin American Journal of Solids and Structures, 8(2), 139-148.

Bazehhour BG, Mousavi SM, Farshidianfar A (2014). Free vibration of high-speed rotating Timoshenko shaft with various boundary conditions: effect of centrifugally induced axial force. Archive of Applied Mechanics, 84 (12), 1691-1700.

Bian X, Cheng C, Jiang J, Chen R, Chen Y (2016). Numerical analysis of soil vibrations due to trains moving at critical speed. Acta Geotechnica, 11(2), 281-294.

Dimitrovová Z (2016). Critical velocity of a uniformly moving load on a beam supported by a finite depth foundation. Journal of Sound and Vibration, 366, 325-342.

Ghannadiasl A (2017). Analytical study of dynamic response of railway on partial elastic foundation under travelling accelerating concentrated load. International Journal of Transportation Engineering, 4(4), 317-334.

Ghannadiasl A, Khodapanah Ajirlou S (2018). Dynamic response of multi-cracked beams resting on elastic foundation. International Journal of Engineering, 31(11), 1830-1837.

Ghannadiasl A, Khodapanah Ajirlou S (2019). Forced vibration of multi-span cracked Euler–Bernoulli beams using dynamic Green function formulation. Applied Acoustics, 148, 484-494.

Gładysz M, Śniady P (2009). Spectral density of the bridge beam response with uncertain parameters under a random train of moving forces. Archives of Civil and Mechanical Engineering, 9(3), 31-47.

Györgyi J (1981). Frequency-dependent geometrical stiffness matrix for the vibration analysis of beam systems. Periodica Polytechnica Civil Engineering, 25(3-4), 151-163.

Hilal MA, Zibdeh HS (2000). Vibration analysis of beams with general boundary conditions traversed by a moving force. Journal of Sound and Vibration, 229(2), 377-388.

Kargarnovin MH, Younesian D (2004). Dynamics of Timoshenko beams on Pasternak foundation under moving load. Mechanics Research Communications, 31(6), 713-723.

Kenney JT (1954). Steady-state vibrations of beam on elastic foundation for moving load. Journal of Applied Mechanics. 21, 359-364.

Li WL (2000). Free vibrations of beams with general boundary conditions. Journal of Sound and Vibration, 237(4), 709-725.

Mehri BA, Davar A, Rahmani O (2009). Dynamic Green function solution of beams under a moving load with different boundary conditions. Scientia Iranica - Transaction B, Mechanical Engineering, 273-279.

Mohammadzadeh S, Mosayebi SA (2015). Dynamic analysis of axially beam on visco-elastic foundation with elastic supports under moving load. International Journal of Transportation Engineering, 2(4), 289-296.

Motaghian SE, Mofid M, Alanjari P (2011). Exact solution to free vibration of beams partially supported by an elastic foundation. Scientia Iranica - Transaction A, Civil Engineering, 18(4), 861.

Prokić A, Bešević M, Lukić D (2014). A numerical method for free vibration analysis of beams. Latin American Journal of Solids and Structures, 11(8), 1432-1444.

Sheng X, Zhong T, Li Y (2017). Vibration and sound radiation of slab high-speed railway tracks subject to a moving harmonic load. Journal of Sound and Vibration, 395, 160-186.

Timoshenko S (1926). Method of analysis of statical and dynamical stresses in rail. Proceedings of the Second International Congress for Applied Mechanics, Zurich Switzerland, 407-418.

Yayli MÖ, Aras M, Aksoy S (2014). An efficient analytical method for vibration analysis of a beam on elastic foundation with elastically restrained ends. Shock and Vibration, 2014.

Ying J, Lu CF, Chen WQ (2008). Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations. Composite Structures, 84(3), 209-219.

Zrnić NĐ, Gašić VM, Bošnjak SM (2015). Dynamic responses of a gantry crane system due to a moving body considered as moving oscillator. Archives of Civil and Mechanical Engineering, 15(1), 243-250.


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