AXIAL FORCE INFLUENCE ON THE RESPONSE TO DISTRIBUTED MOVING LOAD OF TIMOSHENKO BEAM TYPE RESTING ON VLASOV FOUNDATION

Abstract

The axial force influence on the response to a distributed moving loads of Timoshenko beam type resting on bi-parametric foundation of the Vlasov type is investigated in this thesis.The problem is governed by simultaneous second order partial differential equations with variable and singular coefficients. The main objective of this work is to obtain closed form solution to this class of dynamical problem. In order to obtain the solution, a technique based on the method of Galerkin with the series representation of Heaviside function is first used to reduce the equations to second order ordinary differential equations with variable coefficients. Thereafter the transformed equations are simplified using Struble’s asymptotic method. The Laplace transformation technique was then used in conjunction with convolution theory to obtain the solution. The displacement response for moving distributed force and moving distributed mass models for the dynamical problem are calculated for various time t and presented in plotted curves. Foremost, it is found that, the moving distributed force is not an upper bound for the accurate solution of the moving distributed mass problem, which showing that the inertia term must be considered for accurate assessment of the response to moving distributed load of elastic structural members. Analyses further show that increase in the values of the structural parameters such as axial force N, shear modulus G and foundation stiffness K reduces the response amplitudes of uniform Timoshenko beam under moving distributed loads. Finally, for the same natural frequency, the critical speed for the uniform Timoshenko beam traversed by moving distributed force is greater than that under the influence of a moving distributed mass. Hence resonance is reached earlier in the moving distributed mass problem.