Dynamic responses of poroelastic beams with attached mass-spring systems and time-dependent, non-ideal supports subjected to moving loads: An analytical approach

Document Type: Research Paper


1 M.Sc., Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran

2 Professor, Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran


The present study is the first to analyze the dynamic response of a poroelastic beam subjected to a moving force. Moreover, the influences of attached mass-spring systems and non-ideal supports (with local movements in the supporting points or base due to the presence of factors such as gaps, unbalanced masses, and friction or seismic excitations) on the responses were investigated. Non-ideal support experiences time-dependent deflection and moment. To evaluate the effects of both the theory type and the material properties, three models were investigated for the beam with mass-spring attachment and non-ideal supports: i) elastic Euler-Bernoulli-type beam, ii) elastic Timoshenko-type beam, and iii) poroelastic beam. The governing-coupled PDE equations of the forced vibration of the saturated poroelastic beam were analytically solved via Laplace and finite Fourier transforms. The effects of various parameters on the responses were investigated comprehensively and illustrated graphically. The poroelastic nature of the material properties was found to attenuate the vibration amplitude, and it is assumed that the attached mass can considerably affect the vibration pattern.


Main Subjects

[1].Wong J.Y., 2001, Theory of ground vehicles, John Wiley & Sons Inc, New York, Third Edition.
[2].Jazar R.N., 2008, Vehicle Dynamics: Theory and Applications, Springer.
[3]. Ellis B.R., Ji T., 1997, Human–structure interaction in vertical vibrations, In: Proceedings of the Institution of Civil Engineers—Structures and Buildings 122(1): 1–9.
[4].Snowdon J.C., 1966,Vibration of cantilever beams to which dynamic absorbers are attached, Journal of Acoustic Society of America 39: 878.
[5].Lee H.P.,1996, Dynamic response of a beam with a moving mass, Journal of Sound and Vibration 191: 289-294.
[6].Mofid M., Tehranchi A., Ostadhossein A., 2010, On the viscoelastic beam subjected to moving mass, Advance in Engineering Software 41(2): 240-247.
[7].Bulut H., Kelesoglu O., 2010, Comparing numerical methods for response of beams with moving mass, Advances in Engineering Software 41(7-8): 976-980.
[8].Garinei A., 2006, Vibrations of simple beam-like modelled bridge under harmonic moving loads, International Journal of Engineering Science 44(11-12):778-787.
[9].Şimşek M., Kocatürk T., 2009, Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Composite Structures 90(4): 465-473.
[10]. Raftoyiannis I.G., Avraam T.P., Michaltsos G.T., 2014, Analytical models of floating bridges under moving loads, Engineering Structures 68(1): 144-154.
[11]. Şimşek M., 2010, Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Composite Structures 92(10): 2532-2546.
[12]. Wang Y.-M., Chen C.-H., 2012, The transient dynamics of a moving mass traveling on an eccentric path along a finite simple supported inextensible beam, International Journal of Mechanical Sciences 55(1): 118-128.
[13]. Turhan O., 2000, On the fundamental frequency of beams carrying a point mass: Rayleigh approximation versus exact solutions, Journal of Sound and Vibration 230(2): 449-459.
[14]. Chiba M., Sugimoto T.,2003, Vibration characteristics of a cantilever plate with attached spring–mass system, Journal of Sound and Vibration 260(2):237–263.
[15]. Zhang D., CowinS.C., Oscillatory bending of a poroelastic beam, Journal of Mechanics and Physics of Solids42(10): 1575–1599.
[16]. Wang Z.H., Prevost J.H., Coussy O., 2009, Bending of fluid-saturated poroelastic beams with compressible constitutes, International Journalfor Numericaland AnalyticalMethods in Geomechanics 33(4): 425–447.
[17]. Li L.P., Schulgasser K., Cederbaum G., 1998, Large deflection analysis of poroelastic beams, International Journal of Non-Linear Mechanics 33(1): 1-14.
[18]. Biot M.A., 1941, General theory of three-dimensional consolidation, Journal of Applied Physics 12: 155–164.
[19]. Cederbaum G., Li L., Schulgasser K., 2000, Poroelastic structures, Elsevier Science Ltd., Oxford, UK.
[20]. de Boer R., 2003, Reflections on the development of the theory of porous media, AppliedMechanics Reviews 56(6): 27–42.
[21]. Schrefler B.A., 2002, Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solution, Applied Mechanics Reviews 55(4): 351–388.
[22]. Yang X., Li L., 2006, Mathematical model for dynamics of incompressible saturated poroelastic beam and rod (in Chinese), Acta Mech Solida Sinica 27: 159–166.
[23]. Yang X., Wen Q., 2010, Dynamic and quasi-static bending of saturated poroelastic Timoshenko cantilever beam, Applied Mathematics and Mechanics-English Edition 31(8): 995–1008.
[24]. Yi Y., Li L., Xiao Y., 2009, Quasi-static and dynamical bending of a cantilever poroelastic beam, Journal of Shanghai University (English Ed) 13(3): 189–196.
[25]. Niskos D., Theodorakopoulos D., 1994, Flexural vibrations of poroelastic plate, Acta Mechanica 103: 191–203.
[26]. Busse A., Schanz M., Antes B., 2003, A poroelastic Mindlin-plate, Proceedings in Applied Mathematics and Mechanics3(1):260–261.
[27]. Yang S.S.G.Y.X., 2010, Mathematical model for dynamic of incompressible saturated poroelastic Timoshenko beam, Chinese Journal of Solid Mechanics 2010-4.
[28]. Pakdemirli M., Boyaci H., 2002, Effect of non-ideal boundary conditions on the vibrations of continuous systems, Journal of Sound and Vibration 249(4): 815–823.
[29]. Pakdemirli M., Boyaci H., 2003, Non-linear vibrations of a simple–simple beam with a non-ideal support in between, Journal of Sound and Vibration 268(2): 331–341.
[30]. Aydogdu M., Ece M.C., 2006, Buckling and vibration of non-ideal simply supported rectangular isotropic plates, Mechanics Research Communication 33(4):532–540.

[31]. Malekzadeh K., Khalili S.M.R., Abbaspour P., 2010, Vibration of non-ideal simply supported laminated plate on an elastic foundation subjected to in-plane stresses, Composite Structures 92(6): 1478–1484.
[32]. Boyacı H., 2007, Beam vibrations with non-ideal boundary conditions, Springer Proceedings in Physics 111: 97-102.
[33]. Eigoli A.K., Ahmadian M.T., 2011, Nonlinear vibration of beams under nonideal boundary conditions, Acta Mechanica 218(3-4): 259-267.
[34]. Zarfam R., Khaloo A.R., Nikkhoo A., 2013, On the response spectrum of Euler–Bernoulli beams with a moving mass and horizontal support excitation, Mechanics Research Communication 47 :77-83.
[35]. Rao S., 2010, Mechanical vibrations, Prentice Hall, Fifth Edition.
[36]. Sneddon I.N., 1972, The use of integral transforms, McGraw-Hill.
[37]. Fryba L., 1999, Vibration of solids and structures under moving loads, Groningen. Thomas Telford Ltd., London, Third Edition.