On the Vibration of Prismatic Beam with Non Uniform Prestress under Exponential Loads Travelling at Varying Velocities

Abstract

In this paper, the analysis of prismatic beam with non uniform prestress subjected to both constant and exponential loads is investigated. The governing fourth order partial differential equation were analysed to determine the behavior of the system under consideration. The non-homogeneous governing equation is solved by means of Fourier Sine transform and Laplace transformation and convolution theory. The effects of some parameters such as non uniform prestress, elastic foundation and the length coordinates x of the beam are investigated through the numerical illustration of the obtained approximate analytical result are presented in plotted curves. The results show that the response amplitudes of the simply supported prismatic beam decrease as the foundation modulli K increases. Also, the displacements of simply supported prismatic beam resting on elastic foundation, for fixed value of K, decrease as the prestress N increases. Also the transverse deflections of the beam decrease as the length coordinates x decreases under the actions of moving concentrated loads.