response of non-uniform Rayleigh beam resting on bi-parametric subgrades and
subjected to exponentially varying magnitude moving load is investigated in
this paper. The governing equation is fourth order partial differential
equation with variable coefficient. In order to solve this problem, the versatile
Galerkinís method is used to reduce the governing equation to a second order
ordinary differential equation. For the solution of this equation, Laplace
transformation and convolution theorem are employed. Numerical results in
plotted curves are then presented. The results show that response amplitude of
the non-uniform Rayleigh beam decreases as the shear modules (G) increases.
Also, the deflection profile of the beam decreases with an increasing values of
the foundation modulus (k). Furthermore, as the values of the axial force (N),
rotatory inertia R02 and damping coefficient (e) increases, the response amplitudes of the beam
subjected to exponentially varying magnitude moving load decreases. Finally, it
was observed that the non-uniform beam undergoes downward deflection profiles
from the origin when the effects of each of the parameters such as shear
modules, rotatory inertia and damping coefficient on the beam are considered
while upward deflection profiles from the origin when the effects of foundation
modulus and axial force are noticeable.
Keywords: Bi-parametric subgrades, non-uniform beam,
exponentially varying moving load, damping term.