This paper investigates the effect of axial force and rotatory inertial on the dynamic motion of non-uniform Rayleigh beam resting on Pasternak foundation transverseby harmonically varying magnitude moving loads. The versatile Galerkin'smethod and the integral transform techniques were employed to treat the fourth order partial differential equation governing the motion of the vibrating system. Analytical solution was obtained for the transverse displacement response of the non-uniform Rayleigh beam. Analytical and numerical results show that as the values of axial force (N) and rotatory inertial () increases the deflection profile of the non-uniform Rayleigh beam decreases. It is also found that as the values of the other structural parameter such as shear module (G), foundation modulus (K) and damping coefficient () increases lead to decreases in the deflection profile of the beam. Finally, it is observed that the effect of rotatory inertia is significant compared to that of the axial force.

In this study, the effect of rotatory inertia on the transverse motion of uniform Rayleigh beam resting on Pasternak foundation subjected to harmonic magnitude moving load is investigated. We employed Fourier sine transform, Laplace integral transformation and convolution theorem as solution technique. It was observed from the results that, the amplitude of the deflection profile of the beam decreases with increase in the value of rotatory inertia and load natural frequency. Also increases in the values of the other structural parameters like shear modulus, foundation modulus, axial force, and damping coefficient lead to decreases in the deflection profile of the beam. It was also observed that the effect of the load natural frequency is more noticeable than that of the rotatory inertia.

This paper investigates the dynamic behavior of uniform Rayleigh beam resting on Pasternak foundation and subjected to exponentially varying magnitude moving the load. The solution techniques are based on finite Fourier sine transformed Laplace transformation and convolution theorem. The results show that for a fixed value of axial force, damping coefficient and rotatory inertia, increases in shear modulus and foundation modulus reduces the response amplitude of the dynamical system. It was also found that increases in axial force, rotary inertia, and damping coefficient for fixed values of shear modulus and foundation modulus lead to decreases in the deflection profile of the Rayleigh beam resting on Pasternak foundation. Finally, it was found that the effect of shear modulus is more noticeable that of the foundation modulus.