Dynamic Behaviour Under Moving Masses of Prestressed and Elastically Supported Plates Resting on Winkler Foundation
Abstract
The dynamic behaviour of prestressed and elastically supported rectangular plates under moving concentrated masses and resting on Winkler elastic foundation is investigated in this work. This problem involves non-classical boundary conditions; it is solved using a technique based on separation of variables and a modification of Struble's technique, the solution is illustrated with two common examples of non-classical boundary conditions often encountered in engineering practice. The numerical results in plotted curves show that the response amplitudes of the plates decrease as the value of the axial force in x-direction (Nx) increases, the response amplitudes also decrease as axial force in y-direction (Ny) increase for both cases of moving force and moving mass problems of the pre-stressed and elastically supported rectangular plate resting on Winkler elastic foundation for the illustrative examples considered. The deflection of the plate also decreases as the value of the rotatory inertia correction factor R0 increases. Also, for fixed values of Nx and Ny, the transverse deflections of the rectangular plates under the actions of moving masses are higher than those when only the force effects of the moving loads are considered and the critical speed for the moving mass problem is reached prior to that of the moving force problem. It is further shown that the moving force solution is not a safe approximation to the moving mass problem which implies that it is risky to rely on a design based on the moving force solution. The response amplitudes of the moving mass problem increase with increasing mass ratio and approach the response amplitudes of the moving force as the mass ratio approaches zero for the pre-stressed and elastically supported rectangular plates resting on Winkler elastic foundation.
Keywords: Prestress, Rotatory Inertia, Moving Force, Moving Mass, Resonance, Critical speed, Mass Ratio.
References
Fryba, L. (1972): Vibration of solids and structures under moving
loads. Groningen: Noordhoff.
Oni, S. T. (1991): On the dynamic response of elastic structures to
moving multi-mass system. Ph.D. thesis. University of Ilorin,
Nigeria.
Inglis, C. E. (1934): A mathematical treatise on vibration in railway
bridges. The University press, Cambridge.
Gbadeyan, J. A. and Aiyesimi, Y. M. (1990): Response of an
elastic beam resting on viscoelastic foundation to a load
moving at non-uniform speed. Nigerian Journal of
Mathematics and Applications, 3: 73-90.
Sadiku, S. and Leipholz, H. H. E. (1981): On the dynamics of
elastic systems with moving concentrated masses. Ing.
Archiv. 57: 223-242.
Gbadeyan, J. A. and Oni, S. T. (1995): Dynamic behaviour of
beams and rectangular plates under moving loads. Journal of
Sound and Vibration. 182(5): 677-695.
Wilson, J. F. (1974): Dynamic whip of elastically restrained plate
strip to rapid transit loads. Transactions of the American
Society of Mechanical Engineers. Series G. 96: 163-168.
Saito, H., Chonan, S. and Kawanobe, O. (1980): Response of an
elastically supported plate strip to a moving load. Journal of
Sound and Vibration. 71(2): 191-199.
Shadnam, M. R., Mofid, M. and Akin, J. E. (2001): On the
dynamic response of rectangular plate, with moving mass.
Thin-Walled Structures, 39: 797 – 806.
Oni, S. T. (2004): Flexural motions of a uniform beam under the
actions of a concentrated mass traveling with variable
velocity. Abacus, Journal of Mathematical Association of
Nigeria. Vol. 31(2a): 79 – 93.
Oni S. T. and Omolofe B. (2005): Dynamic analysis of a
prestressed elastic beam with general boundary conditions
under moving loads at varying velocities. Journal of
Engineering and Engineering Technology, FUTA, 4(1):
–72.
Oni S. T. and Awodola T. O. (2003): Vibrations under a moving
load of a non-uniform Rayleigh beam on variable elastic
foundation. Journal of Nigerian Association of
Mathematical Physics, 7: 191 – 206.
Omer, C. and Aitung, Y. (2006): Large deflection static analysis
of rectangular plates on two parameter elastic foundations.
International Journal of Science and Technology. 1(1): 43 –
Adams, G. G. (1995): Critical speeds and the response of a
tensioned beam on an elastic foundation to repetitive
moving loads. Int. Jour. Mech. Sci., 7: 773 – 781.
Savin, E. (2001): Dynamics amplification factor and response
spectrum for the evaluation of vibrations of beams under
successive moving loads. Journal of Sound and Vibrations,
(2): 267 – 288.
Jia-Jang, W. (2006): Vibration analysis of a portal frame under
the action of a moving distributed mass using moving mass
element. Int. Jour. for Numerical Methods in Engineering,
: 2028 – 2052.
Oni, S. T. and Awodola, T. O. (2009): Dynamic behaviour under
moving concentrated masses of elastically supported finite
Bernoulli-Euler beam on Winkler foundation. Journal of the
Nigerian Mathematical Society (JNMS). 28: 1-26.
Clough, R. W. and Penziens, J. (1975): Dynamics of structures,
Mcgraw-Hill. Inc.
Awodola, T. O. and Omolofe, B. (2014): Response to concentrated
moving masses of elastically supported rectangular plates
resting on Winkler elastic foundation. Journal of Theoretical
and Applied Mechanics, Sofia, 44(3): 65-90.
Lee, H. P. and Ng, T. Y. (1996): Transverse vibration of a plate
moving over multiple point supports. Applied Acoustics,
(4): 291 – 301.
Oni, S. T. and Ogunbamike, O. K. (2011): Convergence of closed
form solutions of the initial-boundary value moving mass
problem of rectangular plates resting on Pasternak
foundations. Journal of the Nigerian Association of
Mathematical Physics (J. of NAMP), 18: 83-90.
Downloads
Published
Issue
Section
License
Copyright
With the submission of a manuscript, the corresponding author confirms that the manuscript is not under consideration by another journal. With the acceptance of a manuscript, the Journal reserves the exclusive right of publication and dissemination of the information contained in the article. The veracity of the paper and all the claims therein is solely the opinion of the authors not the journal.