Vibrations Of A Simply Supported Plate Under Moving Masses And Resting On Pasternak Elastic Foundation With Stiffness Variation

Abstract

In this investigation, the dynamic behaviour of simply supported rectangular plate carrying moving masses and resting on Pasternak elastic foundation with stiffness variation 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 second order ordinary differential equations. The modified method of Struble and the integral transformations are then employed for the solutions of the reduced equations. Numerical results in plotted curves are then presented. The results show that as the value of the rotatory inertia correction factor Ro increases, the response amplitudes of the plate decrease and for fixed value of Ro, the displacements of the simply supported rectangular plates resting on Pasternak elastic foundations with stiffness variation decrease as the foundation modulus Fo increases. It is also shown that as the value of the shear modulus Go increases the displacement amplitudes of the plate decrease. For fixed Ro, Fo and Go, 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 load are considered. This implies that resonance is reached earlier in moving mass problem than in moving force problem. Furthermore, the result shows that the critical speed increases as Go, Fo and Ro increase, this implies that risk is reduced.