BEHAVIORAL STUDY OF BEAMS ON TWO-PARAMETER SUBGRADE AND UNDER THE ACTIONS OF MOVING DISTRIBUTED MASSES

Abstract

This work concerns the behavioral study of a structural member continuously supported by a two-parameter elastic subgrade and traversed by uniform partially distributed moving masses. The governing equation is a fourth order partial differential equation with variable and singular coefficients. The aim of this study is to obtain approximate analytical solutions of the given problem valid for all variants of boundary conditions of practical interest. In order to obtain these solutions, the spectral Galerkin method is used to reduce the non-homogenous partial differential equation to a sequence of second order ordinary differential equation with variable coefficients. The resulting Galerkin’s equation were then simplified using the modified asymptotic method of struble. The simplified second order ordinary differential equations were then solved using the method of integral transformation. The closed form solutions obtained were analyzed and various results discussed and presented in plotted curves. Results show that an increase in the values of foundation moduli K and shear modulus G, axial force N reduce the response amplitudes of the structural member when under the actions of the travelling masses. It was observed that these structural parameters enhance the stability of the vibrating system. It was also found that for the same natural frequency, the critical speed for the moving distributed mass problem is smaller than that for moving distributed force problem. Hence resonance is reached earlier in the former.