Abstract
In this paper, the nonlinear dynamic response of an inclined pinned-pinned beam with a constant cross section, finite length subjected to a concentrated vertical force traveling with a constant velocity is investigated. The study is focused on the mode summation method and also on frequency analysis of the governing PDEs equations of motion. Furthermore, the steady-state response is studied by applying the multiple scales method. The nonlinear response of the beam is obtained by solving two coupled nonlinear PDEs governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-pint of the beam are obtained for various load velocity ratios and the outcome results have been illustrated and compared to the results with those obtained from traditional linear solution. The appropriate parametric study considering the effects of the linear viscous damping, the velocity of the traveling load, beam inclination angle under zero or nonzero axial load are carried out to capture the influence of the effect of large deflections caused by stretching effects due to the beam’s immovable ends. It was seen that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also in the case where the object leaves the inclined beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption. Moreover, the stability analysis of steady-state response for the modes equations having quadratic nonlinearity was carried out and it was observed from the frequency response curves that for the considered parameters in the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon can be predicted for the longitudinal excitation.
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References
Abuhilal, M., Zibdeh, H.S.: Vibration analysis of beams with general boundary conditions traversed by a moving load. J. Sound Vib. 229(2), 377–388 (2000)
Esmailzadeh, E., Ghorashi, M.: Vibration analysis of beams traversed by uniform partially distributed moving masses. J. Sound Vib. 184(1), 9–17 (1995)
Esmailzadeh, E., Ghorashi, M.: Vibration analysis of a Timoshenko beam subjected to a traveling mass. J. Sound Vib. 199(4), 615–628 (1997)
Foda, M.A., Abduljabbar, Z.: A dynamic green function formulation for the response of a beam structure to a moving mass. J. Sound Vib. 210(3), 295–306 (1998)
Fryba, L.: Vibration of Solids and Structures Under Moving Loads. Thomas Telford, London (1999)
Ichikawa, M., Miyakawa, Y., Matsuda, A.: Vibration analysis of the continuous beam subjected to a moving mass. J. Sound Vib. 230(3), 493–506 (2000)
Ju, S.H., Lin, H.T., Hsueh, H.H., Wang, S.H.: A simple finite element model for vibration analyses induced by moving vehicles. Int. J. Numer. Methods Eng. 68, 1232–1256 (2006)
Kargarnovin, M.H., Younesian, D.: Dynamics of Timoshenko beams on Pasternak foundation under moving load. Mech. Res. Commun. 31, 713–723 (2004)
Kargarnovin, M.H., Younesian, D., Thompson, D.J., Jones, C.J.C.: Response of beams on nonlinear viscoelastic foundations to harmonic moving loads. Comput. Struct. 83, 1865–1877 (2005)
Kidarsa, A., Scott, M.H., Christopher, H.C.: Analysis of moving loads using force-based finite elements. Finite Elem. Anal. Des. 44(4), 214–224 (2008)
Lee, H.P.: The dynamic response of a Timoshenko beam subjected to a moving mass. J. Sound Vib. 198(2), 249–256 (1996)
Lin, Y.H., Trethewey, M.W.: Finite element analysis of elastic beams subjected to moving dynamic loads. J. Sound Vib. 136(2), 323–342 (1990)
Lou, P., Dai, G.L., Zeng, Q.Y.: Finite-element analysis for a Timoshenko beam subjected to a moving mass. J. Mech. Eng. Sci., IMechE 220(C), 669–678 (2006)
Michaltsos, G.T.: Dynamic behavior of a single-span beam subjected to loads moving with variable speeds. J. Sound Vib. 258(2), 359–372 (2002)
Michaltsos, G., Sophianopoulos, D., Kounadis, A.N.: 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 (1996)
Nayfeh, A.H., Mook, D.T.: Nonlinear Oscillations. Wiley-Interscience, New York (1979)
Olsson, M.: On the fundamental moving load problem. J. Sound Vib. 145(2), 299–307 (1991)
Savin, E.: Dynamic amplification factor and response spectrum for the evaluation of vibrations of beams under successive moving loads. J. Sound Vib. 248(2), 267–288 (2001)
Siddiqui, S.A.Q., Golnaraghi, M.F., Heppler, G.R.: Dynamics of a flexible beam carrying a moving mass using perturbation, numerical and time-frequency analysis techniques. J. Sound Vib. 229(5), 1023–1055 (2000)
Simsek, M., Kocaturk, T.: Nonlinear dynamic analysis of an eccentrically prestressed damped beam under a concentrated moving harmonic load. J. Sound Vib. 320, 235–253 (2009)
Thambiratnam, D., Zhuge, Y.: Dynamic analysis of beams on an elastic foundation subjected to moving loads. J. Sound Vib. 198(2), 149–169 (1996)
Wang, R.T.: Vibration of multi-span Timoshenko beams to a moving force. J. Sound Vib. 207(5), 731–742 (1997)
Wang, R.T., Chou, T.H.: Non-linear vibration of Timoshenko beam due to moving force and the weight of beam. J. Sound Vib. 218(1), 117–131 (1998)
Wang, R.T., Lin, J.S.: Vibration of multi-span Timoshenko frames due to moving loads. J. Sound Vib. 212(5), 417–434 (1998)
Wu, J.J.: Dynamic analysis of an inclined beam due to moving loads. J. Sound Vib. 288, 107–133 (2005)
Xu, X., Xu, W., Genin, J.: A non-linear moving mass problem. J. Sound Vib. 204(3), 495–504 (1997)
Yanmeni Wayou, A.N., Tchoukuegno, R., Woafo, P.: Non-linear dynamics of an elastic beam under moving loads. J. Sound Vib. 273, 1101–1108 (2004)
Younesian, D., Kargarnovin, M.H., Thompson, D.J., Jones, C.J.C.: Parametrically excited vibration of a Timoshenko beam on random viscoelastic foundation subjected to a harmonic moving load. Nonlinear Dyn. 45, 75–93 (2006)
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A. Mamandi is a Ph.D. Student.
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Mamandi, A., Kargarnovin, M.H. & Younesian, D. Nonlinear dynamics of an inclined beam subjected to a moving load. Nonlinear Dyn 60, 277–293 (2010). https://doi.org/10.1007/s11071-009-9595-8
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DOI: https://doi.org/10.1007/s11071-009-9595-8