Flexural Motion Under Moving Masses of Prestressed Simply Supported Plate Resting on Bi-Parametric Foundation

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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 G0 and the rotatory inertia correction factor R0 increase. Also, the transverse deflections of the prestressed rectangular plates under the actions of moving masses are higher than those when only the force effects of the moving loads are considered, the analysis of resonance shows that resonance is attained earlier in moving mass problem than in moving force problem and the critical speed for the moving mass problem is reached prior to that of the moving force problem which implies 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.

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