FORCED RESPONSE VIBRATION OF SIMPLY SUPPORTED BEAMS WITH AN ELASTIC PASTERNAK FOUNDATION UNDER A DISTRIBUTED MOVING LOAD

F. A. Hammed; M. A. Usman; S. A. Onitilo; F. A. Alade; K. A. Omoteso

F. A. Hammed Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye
M. A. Usman Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye
S. A. Onitilo Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye
F. A. Alade Department of Mathematical Sciences, Olabisi Onabanjo University, Ago Iwoye
K. A. Omoteso Department of Physics, Olabisi Onabanjo University, Ago Iwoye

Keywords: Dynamic response, Two-parameter Pasternak elastic Foundation, Euler-Bernoulli beam, Moving Force, Foundation Parameter

Abstract

In this study, the response of two homogeneous parallel beams with two-parameter Pasternak elastic foundation subjected to a constant uniform partially distributed moving force is considered. On the basis of Euler-Bernoulli beam theory, the fourth order partial differential equations of motion describing the behavior of the beams when subjected to a moving force were formulated. In order to solve the resulting initial-boundary value problem, finite Fourier sine integral technique and differential transform scheme were employed to obtain the analytical solution. The dynamic responses of the two beams obtained was investigated under moving force conditions using MATLAB. The effects of speed of the moving force, layer parameters such as stiffness (K_0) and shear modulus (G_0 ) have been conducted for the moving force.Various values of speed of the moving load, stiffness parameters and shear modulus were considered. The results obtained indicates that response amplitudes of both the upper and lower beams increases with increase in the speed of the moving load. Increasing the stiffness parameter is observed to cause a decrease in the response amplitudes of the beams. The response amplitudes decreases with increase in the shear modulus of the linear elastic layer.