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Home  >  Volume 26 (March 2014)

19. Flexural Vibrations Under Moving Masses of Rectangular Plates With General Boundary Conditions and Resting on Variable Bi-Parametric Foundation by Awodola T. O. and Oni S. T. Volume26, (March, 2014), pp109 – 124.
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In this paper, the dynamic analysis of rectangular plate, with general classical boundary conditions, carrying moving masses and resting on a bi-parametric (Pasternak) elastic foundation with stiffness variation is considered. The governing equation is a fourth order partial differential equation with variable and singular coefficients, in order to solve the governing equation, a technique based on separation of variables is used to reduce the equation to a sequence of second order ordinary differential equations. The Struble’s technique and the integral transformations are employed for the solutions of the second order ordinary differential equations. The results are then presented in plotted curves. The results show that as the value of the rotatory inertia correction factor Ro increases, the response amplitudes of the plate decrease and that, for fixed value of Ro, the displacements of the plate decrease as the foundation modulus Fo increases for the variants of the classical boundary conditions considered. The results also show that for fixed Ro and Fo, 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. For the rectangular plate, for the same natural frequency, the critical speed for moving mass problem is smaller than that of the moving force problem for all variants of classical boundary conditions, that is, resonance is reached earlier in moving mass problem than in moving force problem, this implies that the moving force solution is not a save approximation to the moving mass problem and hence it is highly risky to rely on the moving force solution as an approximate solution to the moving mass problem. 

Keywords:Pasternak Foundation, Critical speed, Rotatory Inertia, Resonance, Moving Force, Moving Mass, Foundation modulus.