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http://dx.doi.org/10.12989/csm.2014.3.3.247
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A new approach to modeling the dynamic response of Bernoulli-Euler beam under moving load |

Maximov, J.T. (Technical University of Gabrovo, Department of Applied Mechanicas) |

Publication Information

Abstract

This article discusses the dynamic response of Bernoulli-Euler straight beam with angular elastic supports subjected to moving load with variable velocity. A new engineering approach for determination of the dynamic effect from the moving load on the stressed and strained state of the beam has been developed. A dynamic coefficient, a ratio of the dynamic to the static deflection of the beam, has been defined on the base of an infinite geometrical absolutely summable series. Generalization of the R. Willis' equation has been carried out: generalized boundary conditions have been introduced; the generalized elastic curve's equation on the base of infinite trigonometric series method has been obtained; the forces of inertia from normal and Coriolis accelerations and reduced beam mass have been taken into account. The influence of the boundary conditions and kinematic characteristics of the moving load on the dynamic coefficient has been investigated. As a result, the dynamic stressed and strained state has been obtained as a multiplication of the static one with the dynamic coefficient. The developed approach has been compared with a finite element one for a concrete engineering case and thus its authenticity has been proved.

Keywords

Bernoulli-Euler beam; moving load; dynamic stress; dynamic deflection; elastic supports; FE analysis;

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- Reference
- Cited By KSCI

1 | Azam, E., Mofid, M. and Khoraskani, R.A. (2013), "Dynamic response of Timoshenko beam under moving mass", Scientia Iranica, 20 (1), 50-56. |

2 | Abu-Hilal, M. and Zibden, H.S. (2000), "Vibration analysis of beams with general boundary conditions traversed by a moving force", J. Sound Vib., 229(2), 377-388. DOI ScienceOn |

3 | Amiri, S.N. and Onyango, M. (2010), "Simply supported beam response on elastic foundation carrying repeated rolling concentrated loads", J. Eng. Sci. Technol., 5(1) 52-66. |

4 | Awodola, T.O. (2007), "Variable velocity influence on the vibration of simply supported Bernoulli-Euler beam under exponentially varying magnitude moving load", J. Math. Stat., 3(4), 228-232. DOI |

5 | Chonan, S. (1975), "The elastically supported Timoshenko beam subjected to an axial force and a moving load", Int. J. Mech. Sci., 17(9), 573-581. DOI ScienceOn |

6 | Chonan, S. (1978), "Moving harmonic load on an elastically supported Timoshenko beam", J. Appl. Math. Mech., 58 (1), 9-15. |

7 | Clebsch, A. (1883), Theorie de l'elasticite des corps solides, Traduite par Barre de Saint-Venant et A. Flamant, Dunodm, Paris. |

8 | Hilal, M.A. and Mohsen, M. (2000), "Vibration of beams with general boundary conditions due to a moving harmonic load", J. Sound Vib., 232(4), 703-717. DOI ScienceOn |

9 | Ding, H., Chen, L.Q. and Yang, S.P. (2012), "Convergence of Galerkin truncation for dynamic response of finite beams on nonlinear foundations under a moving load", J. Sound Vib., 331, 2426-2442. DOI ScienceOn |

10 | Esmailzadeh, E. and Jalili, N. (2003), "Vehicle-passenger-structure interaction of uniform bridges traversed by moving vehicles", J. Sound Vib., 260, 611-635. DOI ScienceOn |

11 | Friba, L. (1999), Vibration of solid and structures under moving loads, Thomas Telford, London. |

12 | Hillerborg, A. (1951), Dynamic influence of smoothly running loads of simple supported girders, Kungliga Tekniska Hogskolan, Stockholm. |

13 | Hryniewicz, Z. (2011), "Dynamics of Rayleigh beam on nonlinear foundation due to moving load using Adomian decomposition and coiflet expansion", Soil Dyn. Earthq. Eng., 31, 1123-1131. DOI ScienceOn |

14 | Inglis, C.E. (1934), A mathematical treatise on vibration in railway bridges, Cambridge University Press, Cambridge. |

15 | Javanmard, M., Bayat, M. and Ardakani, A. (2013), "Nonlinear vibration of Euler-Bernoulli beams resting on linear elastic foundation", Steel Compos. Struct., 15(4), 439-449. DOI ScienceOn |

16 | Lin, Y.H. and Trethewey, M.W. (1993), "Active vibration suppression of beam structures subjected to moving loads: a feasibility study using finite elements", J. Sound Vib., 166 (3), 383-395. DOI ScienceOn |

17 | Karami-Khorramabadi, M. and Nezamabadi, A.R. (2012), "Dynamic analysis of infinite composite beam subjected to a moving load located on a viscoelastic foundation based on the third order shear deformation theory", J. Basic Appl. Sci. Res., 2(8), 8378-8381. |

18 | Kerr, A.D. (1972), "The continuously supported rail subjected to an axial force and a moving load", Int. J. Mech. Sci., 14(1), 71-78. DOI ScienceOn |

19 | Kien, N.D. and Ha, L.T. (2011), "Dynamic characteristics of elastically supported beam subjected to a compressive axial force and a moving load", Vietnam J. Mech., 33(2), 113-131. |

20 | Krilov, A.N. (1905), "Uber die erzwungenen schwingungen von gleichformigen elastischen staben", Mathematishce Annalen, 61, 211. DOI |

21 | Lin, H.P. and Chang, S.C. (2006), "Forced responses of cracked contilever beam subjected to a concentrated moving load", Int. J. Mech. Sci., 48(12), 1456-1463. DOI ScienceOn |

22 | Lin, Y.H. and Trethewey, M.W. (1990), "Finite element analysis of elastic beams subjected to moving dynamic loads", J. Sound Vib., 136(2), 323-342. DOI ScienceOn |

23 | Liu, Z., Yin, Y., Wang, F., Zhao, Y. and Cai, L. (2013), "Study on modified differential transform method for free vibration analysis of uniform Euler-Bernoulli beam", Struct. Eng. Mech., 48 (5) 697-709. DOI ScienceOn |

24 | Michaltos, G.T. (2002), "Dynamic behaviour of a single-span beam subjected to loads moving with variable speeds", J. Sound Vib., 258(2), 359-372. DOI ScienceOn |

25 | Samani, F. and Pellicano, F. (2009), "Vibration reduction on beams subjected to moving loads using linear and nonlinear dynamic absorbers", J. Sound Vib., 325, 742-754. DOI ScienceOn |

26 | Michaltos, G.T., Sophianopulos, D. and Kounadis, A.N. (1996), "The effect of a moving mass and other parameters on the dynamic response of a simply supported beam", J. Sound Vib., 191(3), 357-362. DOI ScienceOn |

27 | Nikkhoo, A. and Amankhani, M. (2012), "Dynamic behaviour of functionally graded beams traversed by a moving random load", Indian J. Sci. Technol., 5(12), 3727-3731. |

28 | Omolofe, B. (2013), "Deflection profile analysis of beams on two-parameter elastic subgrade", Latin American J. Solids Struct., 10, 263-282. DOI |

29 | Petrov, N.P. (1903), "Influence of the translational velocity of the wheel on the rail stress", Reports of the Imperial Russian Technological Society, 37(2), 27-115 (in Russian). |

30 | Piccardo, G. and Tubino, F. (2012), "Dynamic response of Euler-Bernoulli beams to resonant harmonic moving loads", Struct. Eng. Mech., 44 (5) 681-704. DOI ScienceOn |

31 | Prager, W. and Save, M. (1963), "Minimum-weight design of beams subjected to fixed and moving loads". J. Mech. Physics Solids, 11, 255-267. DOI ScienceOn |

32 | Soares, R.M., del Prado, Z.J.G.N. and Goncales, P.B. (2010), "On the vibration of beams using a moving absorber and subjected to moving loads", Mecanica Comput., (29) 1829-1840. |

33 | Stokes, G.G. (1849), "Discussion of a differential equation relating to the breaking of railway bridges", Transactions of the Cambridge Philosophical Society, 85(5), 707-735. |

34 | Timoshenko , S.P. (1972), Theory of elasticity, Naukova Dumka, Kiev (In Russian) |

35 | Sun, L. and Luo, F. (2008), "Steady-state dynamic response of a Bernoulli-Euler beam on a viscoelastic foundation subjected to a platoon of moving dynamic load", J. Vib. Acoust., 130, 051002-1 - 051002-19. DOI |

36 | Thambiratnam, D. and Zhuge, Y. (1996), "Dynamic analysis of beams on an elastic foundation subjected to moving loads", J. Sound Vib., 198 (2), 149-169. DOI ScienceOn |

37 | Timoshenko, S.P. (1922), "On the forced vibrations of bridges", Philosophical Magazine Series 6, 43(257), 1018-1019. DOI |

38 | Willis, R. (1849), Report of the commissioners appointed to inquire into the application of iron to railway structures, William Clowes & Sons, London. |

39 | Wu, J.J. (2005), "Dynamic analysis of inclined beam due to moving load", J. Sound Vib., 288(1-2), 107-131. DOI ScienceOn |

40 | Zehsaz, M., Sadeghi, M.H. and Asl, A.Z. (2009), "Dynamic Response of railway under a moving load", J. Appl. Sci., 9(8), 1474-1481. DOI |

41 | Xia, H., Zhang, N. and Guo, W.W. (2006), "Analysis of resonance mechanism and conditions of train-bridge system", J. Sound Vib., 297, 810-822. DOI ScienceOn |

42 | Yang, Y.B., Yau, J.D. and Hsu, L.C. (1997), "Vibration of simple beams due to trains moving at high speeds", Eng. Struct., 19(11), 936-944. DOI ScienceOn |

43 | Yau, J.D. (2004), "Vibration of simply supported compound beams to moving loads", J. Marine Sci. Technol., 12(4), 319-328. |

44 | Zheng, D.Y., Cheung, Y.K., Au, F.T.K. and Cheng, Y.S. (1998), "Vibration of multi-span non-uniform beams under moving loads by using modified beam vibration functions", J. Sound Vib., 212(3), 455-467. DOI ScienceOn |

45 | Mehril, B., Davar, A. and Rahmani, O. (2009), "Dynamic Green function solution of beams under a moving load with different boundary conditions", J. Sharif Univ. of Technol., Transaction B: Mech.Eng., 16(3), 273-279. |

46 | Zibdeh, H.S. and Rackwitz, R. (1995), "Response moments of an elastic beam subjected to Poissonian moving loads", J. Sound Vib., 188 (4), 479-495. DOI ScienceOn |