Author(s): Gabriel Ojonugwa Jacobs, Baba Wachiko, Musa Bawa, Salisu Abdullahi, and Oyetade Sunday Adewuyi

Comparative study of non-uniform Rayleigh beam with variable axial force resting on bi-parametric elastic foundations under the actions of moving concentrated and distributed loads was investigated in this project work. In order to obtain the solutions to the fourth order non-homogeneous partial differential equation governing the dynamical problem, the Galerkin Method (GM) was first used to reduce the fourth order partial differential equation into a second order ordinary differential equation. Then, the resulted equation was further treated using the Laplace transform method in conjunction with Convolution theorem to obtain the analytical approximate solutions. Finally, the Maple computer simulation software was used to present the results of the transverse displacement response to the non-uniform Rayleigh beam under the actions of moving concentrated and distributed loads. The results in plotted curves reveals that for both moving concentrated and distributed loads, the deflection profiles of the beam decreases as the values of the structural parameters such as axial force , foundation stiffness , shear modulus , damping coefficient , and rotatory inertia correction factor increases. Also, the deflection profiles of non-uniform Rayleigh beam under the actions of moving distributed loads is higher than that under the actions of moving concentrated loads.