Response characteristics analysis of a simply supported double-beam system under harmonic variable magnitude travelling load

Abstract

In this study, dynamic characteristics of a simply supported double-beam system under the actions of harmonic variable magnitude travelling load was investigated. The system is made up of two parallel prismatic thick beams connected constantly by a layer of viscoelastic material. The governing equations describing the motion of this double-beam when under the actions of a moving load is a set of two fourth order non homogeneous partial differential equations with singular and variable coefficients. To solve this coupled partial differential equations, a versatile method of solution capable of treating this class of problem for all variants of boundary conditions is employed. This involves the application of the Generalized Fourier Sine Transform Method (GFSTM), in conjunction with a modified Asymptotic Method of Struble (AMS) and the Differential Transform Method (DTM). The GFSTM was employed in the first instance to transform the set of partial differential equations of order four governing the motions of the structural members into a sequence of coupled second order ordinary differential equations. The transformed coupled ordinary differential equations was further simplified using AMS. The differential transform method was finally applied to obtain a mathematical expressions representing the coordinates in modal space. Thus, an approximate analytical solutions representing the displacement amplitude of the double-beam system under the action of the traversing load was obtained for the moving force and moving mass models respectively. Analysis of the approximate analytical solutions was presented. Various results were discussed and displayed in plotted curves. Effects of some vital load and structural parameters on the response characteristics of the beam-load system were examined and presented. Conditions under which the systems experiences resonance phenomenon were established and reported.