Dynamic Behaviour Of Non-Prismatic Rayleigh Beam On Pasternak Foundation And Under Partially Distributed Masses Moving At Varying Velocities

Abstract

The dynamic analysis of the behaviour of Non-prismatic Rayleigh beam on Pasternak foundation under partially distributed masses moving at varying velocities is investigated in this paper. The solution technique is based on the expansion of Heaviside function in series form, the use of the generalized Galerkin method and a modification of Struble’s asymptotic method which reduces the governing fourth order partial differential equation to a coupled second order ordinary differential equation. Closed form solutions are obtained and numerical results in plotted curves are presented. The results show that as the value of rotatory inertia correction factor r0 increases, the response amplitude of the Rayleigh beam decreases. Similarly, higher values of the foundation stiffness K, shear modulus G and axial force N decrease the transverse deflection of the beam. The results further show that for fixed r0,K, G and N, the transverse deflection of the non-uniform Rayleigh beam resting on Pasternak foundation and under partially distributed masses moving at varying velocities are higher than those when only the force effects of the moving load are considered indicating clearly that resonance is reached earlier in moving distributed mass problem. This further confirms results in literature stressing the need to always consider the inertia terms when heavy loads traverse any form of structural members.