Browse > Article
http://dx.doi.org/10.12989/sem.2018.66.3.387

A general closed-form solution to a Timoshenko beam on elastic foundation under moving harmonic line load  

Luo, Wei-Li (School of Civil Engineering, Guangzhou University)
Xia, Yong (Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University)
Zhou, Xiao-Qing (College of Civil Engineering, Guangzhou University)
Publication Information
Structural Engineering and Mechanics / v.66, no.3, 2018 , pp. 387-397 More about this Journal
Abstract
In this paper, a general closed-form solution for evaluating the dynamic behavior of a Timoshenko beam on elastic foundation under a moving harmonic line load is formulated in the frequency-wavenumber domain and in a moving coordinate system. It is found that the characteristic equation is quartic with real coefficients only, and its poles can be presented explicitly. This enables the substitution of these poles into Cauchy's residue theorem, leading to the general closed-form solution. The solution can be reduced to seven existing closed-form solutions to different sub-problems and a new closed-form solution to the subproblem of a Timoshenko beam on an elastic foundation subjected to a moving quasi-static line load. Two examples are included to verify the solution.
Keywords
closed-form solution; beam on elastic foundation; moving load; Timoshenko beam; Cauchy's residue theorem;
Citations & Related Records
Times Cited By KSCI : 3  (Citation Analysis)
연도 인용수 순위
1 Calim, F.F. (2016), "Dynamic response of curved Timoshenko beams resting on viscoelastic foundation", Soil Dyn. Earthq. Eng., 59(4), 761-774.
2 Chen, Y.H. and Huang, Y.H. (2000), "Dynamic stiffness of infinite Timoshenko beam on viscoelastic foundation in moving coordinate", Int. J. Numer. Meth. Eng., 48(1), 285-298.
3 Chen, Y.H., Huang, Y.H. and Shih, C.T. (2001), "Response of an infinite Timoshenko beam on a viscoelastic foundation to a harmonic moving load", J. Sound Vibr., 241(5), 809-824.   DOI
4 Fryba, L. (1999), Vibration of Solids and Structures under Moving Loads, Telford, London, U.K.
5 Galvin, P., Francois, S., Schevenels, M., Bongini, E., Degrande, G. and Lombaert, G. (2010), "A 2.5 D coupled FE-BE model for the prediction of railway induced vibrations", Soil Dyn. Earthq. Eng., 30(12), 1500-1512.   DOI
6 Karahan, M.M. and Pakdemirli, M. (2017), "Vibration analysis of a beam on a nonlinear elastic foundation", Struct. Eng. Mech., 62(2), 171-178.   DOI
7 Gan, B.S., Trinh, T.H., Le, T.H. and Nguyen, D.K. (2015), "Dynamic response of non-uniform Timoshenko beams made of axially FGM subjected to multiple moving point loads", Struct. Eng. Mech., 53(5), 981-995.   DOI
8 Hao, H. and Ang, T.C. (1998), "Analytical modeling of trafficinduced ground vibrations", J. Eng. Mech., 124(8), 921-928.   DOI
9 Irving, R.S. (2003), Integers, Polynomials, and Rings: A Course in Algebra, Springer Science & Business Media.
10 Kargarnovin, M. and Younesian, D. (2004), "Dynamics of timoshenko beams on Pasternak foundation under moving load", Mech. Res. Commun., 31(6), 713-723.   DOI
11 Kausel, E. and Roesset, J.M. (1992), "Frequency domain analysis of undamped systems", J. Eng. Mech., 118(4), 721-734.   DOI
12 Kenney, J. (1954), "Steady-state vibrations of beam on elastic foundation for moving load", J. Appl. Mech., 21(4), 359-364.
13 Kim, S.M. (2005), "Stability and dynamic response of Rayleigh beam-columns on an elastic foundation under moving loads of constant amplitude and harmonic variation", Eng. Struct., 27(6), 869-880.   DOI
14 Kim, S.M. and Cho, Y.H. (2006), "Vibration and dynamic buckling of shear beam-columns on elastic foundation under moving harmonic loads", Int. J. Sol. Struct., 43(3), 393-412.   DOI
15 Luo, W.L. and Xia, Y. (2017), "Vibration of infinite timoshenko beam on Pasternak foundation under vehicular load", Adv. Struct. Eng., 20(5), 24-34.
16 Shmakov, S.L. (2011), "A universal method of solving quartic equations", Int. J. Pure Appl. Math., 71(2), 251-259.
17 Luo, W.L., Xia, Y. and Weng, S. (2005), "Vibration of timoshenko beam on hysteretically damped elastic foundation subjected to moving load", Sci. Chin. Phys. Mech., 58(8), 1-9.
18 Luo, W.L., Xia, Y. and Zhou, X.Q. (2016), "A closed-form solution to a viscoelastically supported Timoshenko beam under harmonic line load", J. Sound Vibr., 369(5), 109-118.   DOI
19 Mathews, P.M. (1958), "Vibrations of a beam on elastic foundation", J. Appl. Maths. Mech., 38(3-4), 105-115.
20 Sun, L. (2001), "A closed-form solution of a Bernoulli-Euler beam on a viscoelastic foundation under harmonic line loads", J. Sound Vibr., 242(4), 619-627.   DOI
21 Sun, L. (2002), "A closed-form solution of beam on viscoelastic subgrade subjected to moving loads", Comput. Struct., 80(1), 1-8.   DOI
22 Sun, L. (2003), "An explicit representation of steady state response of a beam on an elastic foundation to moving harmonic line loads", Int. J. Numer. Anal. Met., 27(1), 69-84.   DOI