DYNAMIC RESPONSE TO MOVING CONCENTRATED MASSES OF RAYLEIGH BEAMS ON VARIABLE WINKLER ELASTIC FOUNDATIONS

Abstract

The response of Rayleigh beams carrying moving masses, resting on variable Winkler elastic foundations is investigated in this thesis. The problem is investigated for both cases of uniform and non-uniform Rayleigh beams. In each case, the governing equation is a fourth order partial differential equation. In order to solve this problem, the versatile Galerkin's method is used to reduce the governing fourth order partial differential equations with variable coefficients to a sequence of second order ordinary differential equations. For the solutions of these equations, a modification of the Struble's technique is employed. Numerical results in plotted curves are then presented. The results show that response amplitudes of the uniform Rayleigh beam decrease as the rotatory inertia correction factor R° increases for all variants of classical boundary conditions considered. These same results obtain for the non-uniform Rayleigh beams. Furthermore, for fixed value of R0,the displacements of both uniform and non-uniform Rayleigh beams resting on variable elastic foundations decrease as the foundation modulli K increases. ".' The results further show that, for fixed RO and K, the transverse deflections of both uniform and non-uniform Rayleigh beams under the actions of moving masses are higher than those when only the force effects of the moving load are considered. Therefore, the moving force solution is not a safe approximation to the moving mass problem. Hence safety is not guaranteed for a design based on the moving force solution. Also the analyses show that the response amplitudes of both moving force and moving mass problems decrease both with increasing Foundation constant and with increasing Rotatory inertia. Finally, the critical speed for the moving mass problem is reached prior to that of the moving force for both uniform and non-uniform Rayleigh beam problems in all variants of illustrative examples considered.