Dynamical Analysis of Non Prismatic Rayleigh Beam Resting on NonWinkler Foundation and Subjected to Traveling Distributed Forces

Abstract

The dynamic response of a simply supported non prismatic Rayleigh beam under distributed moving forces resting on Winkler elastic foundation with exponential stiffness is investigated. For the solution of the fourth order partial differential equation with singular and variable coefficients, use is made of the technique based on the Galerkin’s method, integral transformation and convolution theory. The numerical results are presented in plotted curves. The results show that the response amplitudes of the simply supported nonprismatic Rayleigh beam decrease as the foundation modulli Fs increase. Also, the displacements of simply supported non-prismatic Rayleigh beam resting on Winkler elastic foundation, for fixed value of Fs , decrease as the prestress N increases. Also the transverse deflections of the beam decrease as the length coordinate x decreases under the actions of moving distributed loads. The results show that the critical speed for the moving constant load case is reached earlier than that for the harmonic variable moving load.