Dynamic Analysis of an Exponentially Decaying Foundation on the Response of Non-Uniform Damped Rayleigh Beam under Harmonic Moving Load with General Boundary Conditions

Abstract

This study investigates the dynamic response of a non-uniform damped Rayleigh beam on an exponentially decaying foundation subjected to a harmonic moving load with general boundary conditions. The governing equation, a fourth-order non-homogeneous partial differential equation with variable coefficients, is discretized using the Generalized Galerkin Method. Two cases are examined: moving force and moving mass. Closedform solutions are obtained for the moving force case using Laplace transform in conjuction with convolution theorem. For the moving mass case, the Struble asymptotic method cannot simplify the equation for the moving mass case due to the variable load magnitude, and thus, Runge-Kutta method of order four (RK4) is employed to obtain a numerical solution. Analytical and numerical solutions are compared for validation of accuracy of the Runge-kutta scheme and found compared favourably. The effects of some key structural parameters on dynamic behavior are examined, and resonance conditions are established.