FLEXURAL MOTION UNDER MOVING MASSES OF PRESTRESSED SIMPLY SUPPORTED PLATE RESTING ON BI-PARAMETRIC FOUNDATION
Keywords:
Prestress, Rotatory Inertia, Bi-parametric Foundation, Resonance, Critical speed, Mass Ratio.Abstract
In this investigation, the flexural vibration of a prestressed and simply supported rectangular plate carrying moving concentrated masses and resting on bi-parametric (Pasternak) elastic foundation is considered. In order to solve the governing fourth order partial differential equation, a technique based on separation of variables is used to reduce the equation with variable and singular coefficients to a sequence of coupled second order ordinary differential equations. The modified method of Struble and the integral transformations are then employed for the solutions of the reduced equations. The numerical results in plotted curves show that as the value of the axial force in x-direction (Nx) increases, the response amplitudes of the plates decrease, the same effect is produced as the axial force in y-direction (Ny) increases for both cases of moving force and moving mass problems of the prestressed and simply supported rectangular plate resting on Pasternak elastic foundation. The deflection of the plate also decreases in each case as the values of the Shear modulus Go and the rotatory inertia correction factor Ro increase. Also, the transverse deflections of the prestressed rectangular plates under the actions of moving masses are higher than those obtained when only the force effects of the moving loads are considered. Further analysis shows that resonance is attained earlier in moving mass problem than in moving force problem and that the critical speed for the moving mass problem is reached prior to that of the moving force problem, implying that it is risky to rely on a design based on the moving force solution. Furthermore, the response amplitudes of the moving mass problem increase with increasing mass ratio and approach those of the moving force as the mass ratio approaches zero for the prestressed and simply supported rectangular plates resting on uniform Pasternak elastic foundation
References
2. Oni, S. T. (1991): On the dynamic response of elastic structures to moving multi-mass system. Ph.D. thesis. University of Ilorin, Nigeria.
3. Inglis, C. E. (1934): A mathematical treatise on vibration in railway bridges. The University press, Cambridge.
4. 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, Vol.3, pp 73-90.
5. Sadiku, S. and Leipholz, H. H. E. (1981): On the dynamics of elastic systems with moving concentrated masses. Ing. Archiv. 57, 223-242.
6. 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), pp 677-695.
7. Franklin, J. N. and Scott, R. F. (1979): Beam equation with variable foundation coefficient. ASCE. Eng. Mech. Div. Vol. 105, EMS, pp 811-827.
8. Lentini, M. (1979): Numerical solution of the beam equation with non-uniform foundation coefficient. ASME. Journal of Applied Mechanics.Vol.46.pp 901-902.
9. S. T. Oni and T. O. Awodola. (2005): Dynamic response to moving concentrated masses of uniform Rayleigh beams resting on variable Winkler elastic foundation. Journal of the Nigerian Association of Mathematical Physics. Vol. 9. pp 151-162.
10. S. T. Oni, and T. O. Awodola (2010): Dynamic response under a moving load of an elastically supported non-prismatic Bernoulli-Euler beam on variable elastic foundation. Latin American Journal of Solids and Structures. 7, pp 3 - 20.
11. Moshe Eisenberger and Jose Clastornik. (1987): Beams on variable Two-Parameter elastic foundation. Journal of Engineering Mechanics, Vol. 113, No. 10, pp 1454-1466.
12. Gbadeyan, J. A. and Oni, S. T. (1992): Dynamic response to a moving concentrated masses of elastic plates on a non-Winkler elastic foundation. Journal of Sound and Vibration, 154, pp 343-358.
13. Clough Ray W. and Penziens, J (1975): Dynamics of structures, Mcgraw-Hill. Inc.
14. Clastornic, J., Eisenberger, M., Yankelevsky, D. Z. and Adin, M. A. (1986): Beams on variable elastic foundation.
Journal of Applied Mechanics, Vol. 53, pp 925-928.
15. M. R. Shadnam, M. Mofid and J. E. Akin (2001): On the dynamic response of rectangular plate, with moving mass.
Thin-Walled Structures, 39(2001), pp 797 – 806.
16. H. P. Lee and T. Y. Ng (1996): Transverse vibration of a plate moving over multiple point supports. Applied
Acoustics, Vol. 47, No. 4, pp 291 – 301.
17. Oni, S. T. and Awodola, T. O. (2011): Dynamic behaviour under moving concentrated masses of simply supported
rectangular plates resting on variable Winkler elastic foundation. Latin American Journal of Solids and Structures (LAJSS), 8(2011), pp 373 – 392.
18. S. T. Oni and O. K. Ogunbamike (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), Vol. 18 (May, 2011), pp. 83-90.
19. Awodola, T. O. and Omolofe, B. (2016): Flexural motion of elastically supported rectangular plates under concentrated moving masses and resting on bi-parametric elastic foundation. Journal of Vibration Engineering and Technologies (JVET), (Accepted in May, 2016.
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