Dynamic Behaviour Under Moving Masses of Prestressed and Elastically Supported Plates Resting on Winkler Foundation

Authors

  • T. O. Awodola Federal University of Technology Akure

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.

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Published

2019-04-02