Dynamic Behavior Analysis of a Geometrically Nonlinear Plate Subjected to a Moving Load
Subject Areas : Engineering
1 - Department of Mechanical Engineering, Parand Branch, Islamic Azad University, Parand, Iran
2 - Department of Mechanical Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran
Keywords: Moving load, Nonlinear response, Galerkin&rsquo, s method, Plate,
Abstract :
In this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations. Then the Galerkin’s method is used to transform the equations of motion into the three coupled nonlinear ordinary differential equations (ODEs) and then are solved in a semi-analytical way to get the dynamical responses of the plate under the traveling load. A parametric study is conducted by changing the size of moving mass/force and its velocity. Finally, the dynamic magnification factor and normalized time histories of the plate central point are calculated for various load velocity ratios and outcome nonlinear results are compared to the results from linear solution.
[1] Amabili M., 2004, Nonlinear vibrations of rectangular plates with different boundary conditions: theory and experiments, Computers and Structures 82: 2587-2605.
[2] Eftekhari S.A., Jafari A.A., 2012, Vibration of an initially stressed rectangular plate due to an accelerated traveling mass, Scientia Iranica 19(5):1195-1213.
[3] Fryba L., 1999, Vibration of Solids and Structures under Moving Loads, Thomas Telford Publishing, London.
[4] Gbadeyan J.A., Oni S.T., 1995, Dynamic behaviour of beams and rectangular plates under moving loads, Journal of Sound and Vibration 182(5): 677-695.
[5] Ghafoori E., Kargarnovin M.H., Ghahremani A.R., 2010, Dynamic responses of rectangular plate under motion of an oscillator using a semi-analytical method, Journal of Vibration and Control 17(9): 1310-1324.
[6] Kiani K.A., Nikkhoo A., Mehri B., 2009, Prediction capabilities of classical and shear deformable beam models excited by a moving mass, Journal of Sound and Vibration 320: 632-648.
[7] Leissa A.W., 1969, Vibration of Plates, US Government Printing Office, Washington.
[8] Mamandi A., Kargarnovin M.H., Younesian D., 2010, Nonlinear dynamics of an inclined beam subjected to a moving load, Nonlinear Dynamics 60(3): 277-293.
[9] Mamandi A., Kargarnovin M.H., 2014, An investigation on dynamic analysis of a Timoshenko beam with geometrical nonlinearity included resting on a nonlinear viscoelastic foundation and traveled by a moving mass, Shock and Vibration 242090:1-10.
[10] Mamandi A., Kargarnovin M.H., Farsi S., 2014, Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity, Journal of Mathematical Sciences 201(3): 361-383.
[11] Mamandi A., Kargarnovin M.H., 2011, Nonlinear dynamic analysis of an inclined Timoshenko beam subjected to a moving mass/force with beam’s weight included, Shock and Vibration 18(6): 875-891.
[12] Mamandi A., Kargarnovin M.H., 2011, Dynamic analysis of an inclined Timoshenko beam travelled by successive moving masses/forces with inclusion of geometric nonlinearities, Acta Mechanica 218(1):9-29.
[13] Mamandi A., Kargarnovin M.H., Farsi S., 2010, An investigation on effects of a traveling mass with variable velocity on nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions, International Journal of Mechanical Sciences 52(12):1694-1708.
[14] Mamandi A., Kargarnovin M.H., 2013, Nonlinear dynamic analysis of an axially loaded rotating Timoshenko beam with extensional condition included subjected to general type of force moving along the beam length, Journal of Vibration and Control 19(16): 2448-2458.
[15] Meirovitch L., 1997, Principles and Techniques of Vibrations, Prentice-Hall Inc., New Jersey.
[16] Nayfeh A.H., Mook D.T., 1995, Nonlinear Oscillations, Wiley-Interscience, New York.
[17] Nikkhoo A., Rofooei F.R., 2012, Parametric study of the dynamic response of thin rectangular plates traversed by a moving mass, Acta Mechanica 223: 15-27.
[18] Shadnam M.R., Mofid M., Akin J.E., 2001,On the dynamic response of rectangular plate with moving mass, Thin-walled Structures 39: 797-806.
[19] Timoshenko S.P., 1959, Theory of Plates and Shells, Mc Graw-Hill, New York.
[20] Vaeseghi Amiri J., Nikkhoo A., Davoodi M.R., Ebrahimzadeh Hassanabadi M., 2013, Vibration analysis of a Mindlin elastic plate under a moving mass excitation by eigenfunction expansion method, Thin-Walled Structures 62: 53-64.
[21] Wu J.J., 2007,Vibration analyses of an inclined flat plate subjected to moving loads, Journal of Sound and Vibration 299: 373-387.
[22] Yanmeni Wayou A.N., Tchoukuegno R., Woafo P., 2004, Non-linear dynamics of an elastic beam under moving loads, Journal of Sound and Vibration 273: 1101-1108.
[23] Mamandi A., Kargarnovin M.H., Mohsenzadeh R., 2015, Nonlinear dynamic analysis of a rectangular plate subjected to accelerated/decelerated moving load, Journal of Theoretical and Applied Mechanics 53(1):151-166.