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A Gao beam subjected to a moving inertial point load. (English) Zbl 1404.74058
Summary: A model for the dynamics of a Gao elastic or viscoelastic nonlinear beam that is subject to a horizontally moving vertical point-force is modeled and computationally studied. In particular, the behavior and vibrations of the beam as the mass is moving on it is investigated. Such problems arise naturally in transportation systems with rails. A time-marching finite element numerical algorithm for the problem is developed and implemented. Results of representative simulations are depicted and compared to the behavior of a linear Euler beam with a moving mass.

74H45 Vibrations in dynamical problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74S05 Finite element methods applied to problems in solid mechanics
Full Text: DOI
[1] [1] Dahlberg, T . Track issues. In: Iwnicki, S (ed.) Handbook of railway vehicle dynamics. Boca Raton, FL: CRC Press, 2006, 143-180.
[2] [2] Bajer, CI, Bogacz, R. Propagation of perturbances generated in classic track, and track with Y-type sleepers. Arch Appl Mech 2005; 74: 754-761. · Zbl 1158.74372
[3] [3] Bajer, CI, Dyniewicz, B. Numerical modelling of structure vibrations under inertial moving load. Arch Appl Mech 2009; 79(6-7): 499-508. · Zbl 1264.74086
[4] [4] Matej, J. A new mathematical model of the behaviour of a four-axle freight wagon with UIC single-link suspension. Proc IMechE F J Rail Rapid Trans 2011; 225(6): 637-647.
[5] [5] Dyniewicz, B, Konowrocki, R, Bajer, C. Intelligent adaptive control of the vehicle-span/track system. Mech Syst Sign Process 2015; 53(1): 1-14.
[6] [6] Gao, D. Nonlinear elastic beam theory with application in contact problems and variational approaches. Mech Res Commun 1996; 23(1): 11-17. · Zbl 0843.73042
[7] [7] Gao, D, Russell, D. An extended beam theory for smart materials applications part II: Static formation problems. Appl Math Optim 1998; 38(1): 69-94. · Zbl 0911.35039
[8] [8] Gao, D. Finite deformation beam models and triality theory in dynamical post-buckling analysis. Int J Non-Lin Mech 2000; 35: 103-131. · Zbl 1068.74569
[9] [9] Russell, D, White, L. A nonlinear elastic beam system with inelastic contact constraints. Appl Math Optim 2002; 46: 291-312. · Zbl 1076.74029
[10] [10] M’Bengue, M. Analysis of a nonlinear dynamic beam with material damage or contact. PhD Thesis, Oakland University, MI, 2008.
[11] [11] Andrews, K, M’Bengue, M, Shillor, M. Vibrations of a nonlinear dynamic beam between two stops. Discr Cont Dyn Syst (DCDS-B) 2009; 12(1): 23-38. · Zbl 1167.74019
[12] [12] M’Bengue, M, Shillor, M. Regularity result for the problem of vibrations of a nonlinear beam. Electron J Diff Eq 2008; 2008(27): 1-12.
[13] [13] Kuttler, K, Purcell, J, Shillor, M. Analysis and simulations of a contact problem for a nonlinear dynamic beam with a crack. Q J Mech Appl Math 2012; 65(1): 1-25. · Zbl 1248.74032
[14] [14] Andrews, K, Dumont, Y, M’Bemgue, MF. Analysis and simulations of a nonlinear dynamic beam. J Appl Math Phys (ZAMP) 2012; 63(6): 1005-1019.
[15] [15] Ahn, J, Kuttler, K, Shillor, M. Dynamic contact of two Gao beams. Electron J Diff Eq 2012; 2012(194): 1-42. · Zbl 1302.74116
[16] [16] Andrews, K, Kuttler, K, Shillor, M. Dynamic Gao beam in contact with a reactive or rigid foundation. In: Han, W, Migorski, S, Sofonea, M (eds) Advances in variational and hemivariational inequalities with applications (Advances in Mechanics and Mathematics (AMMA), vol. 33). Cham, Switzerland: Springer International, 2015, 225-248. · Zbl 1317.74049
[17] [17] Shillor, M, Sofonea, M, Telega, J. Lecture notes in physics, vol. 655. Berlin: Springer, 2004.
[18] [18] Bajer, C, Bohatier, C. The soft way method and the velocity formulation. Comput Struct 1995; 55(6): 1015-1025. · Zbl 0918.73067
[19] [19] Dyniewicz, B. Space-time finite element approach to general description of a moving inertial load. Fin Elem Anal Des 2012; 62: 8-17.
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