Dynamic analysis of Non-Uniform Rayleigh beam Resting on Bi-Parametric Subgrade under Exponentially Varying Moving Loads

摘要

The response of non-uniform Rayleigh beam resting on bi-parametric subgrades andsubjected to exponentially varying magnitude moving load is investigated in thispaper. The governing equation is fourth order partial differential equation withvariable coefficient. In order to solve this problem, the versatile Galerkin’s methodis used to reduce the governing equation to a second order ordinary differentialequation. For the solution of this equation, Laplace transformation and convolutiontheorem are employed. Numerical results in plotted curves are then presented. Theresults show that response amplitude of the non-uniform Rayleigh beam decreasesas the shear modules (G) increases. Also, the deflection profile of the beamdecreases with an increasing values of the foundation modulus (k). Furthermore, asthe values of the axial force (N), rotatory inertia (?? 02 ), and damping coefficient (??)increases, the response amplitudes of the beam subjected to exponentially varyingmagnitude moving load decreases. Finally, it was observed that the non-uniformbeam undergoes downward deflection profiles from the origin when the effects ofeach of the parameters such as shear modules, rotatory inertia and dampingcoefficient on the beam are considered while upward deflection profiles from theorigin when the effects of foundation modulus and axial force are noticeable.