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Home  >  Volume 28. No.2 (Nov. 2014)

14. Mass Ratio Influence on the Response to Moving Masses of Prestressed Simply Supported Plate Resting on Winkler Foundation by Awodola T. O. - Volume28, No. 2, (November, 2014), pp 81 – 92
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The influence of mass ratio and prestress (axial force) on the response of prestressed simply supported rectangular plates carrying movingmasses and resting on Winkler elastic foundations is investigated in this work. In order to solve the governing fourth order partial differential equation with variable and singular coefficients, a technique based on separation of variables is used to reduce  the equation to a sequence of second order ordinary differential equations. For the solutions of these equations, a modification of the Struble’s technique and method  of integral transformations are employed. The numerical results in plotted curves show that the response amplitudes of the moving mass problem increase with increasingmass ratio and approach the 

response amplitudes of the moving force as the massratio approaches zero for the 

prestressed simply supported rectangular plates resting on Winkler elastic foundation. 

Also, the response amplitudes of the plate decreaseas the value of the axial force in x-direction (Nx) increases, the axial force in y-direction (Ny) produces the same effect 

but the influence of Nx is more noticeable than that of Ny for both cases of moving force and moving mass problems. Furthermore, 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. 

Therefore, the moving force solution is not a safe approximation to the moving mass problem. The results also show that the critical speed for the moving mass problem is reached prior to that of the moving force problem; hence, it is risky to rely on a design based on the moving force solution