Abstract
In this study, the response of two homogeneous parallel beams with two-parameter Pasternak elastic foundation subjected to a constant uniform partially distributed moving force is considered. On the basis of Euler-Bernoulli beam theory, the fourth order partial differential equations of motion describing the behavior of the beams when subjected to a moving force were formulated. In order to solve the resulting initial-boundary value problem, finite Fourier sine integral technique and differential transform scheme were employed to obtain the analytical solution. The dynamic responses of the two beams obtained was investigated under moving force conditions using MATLAB. The effects of speed of the moving force, layer parameters such as stiffness (K_0) and shear modulus (G_0 ) have been conducted for the moving force. Various values of speed of the moving load, stiffness parameters and shear modulus were considered. The results obtained indicates that response amplitudes of both the upper and lower beams increases with increase in the speed of the moving load. Increasing the stiffness parameter is observed to cause a decrease in the response amplitudes of the beams. The response amplitudes decreases with increase in the shear modulus of the linear elastic layer.
Highlights
This work is concerned with the study of elastic beams
In an attempt to eliminate the shortcoming attributed to one-parameter foundation model, an improved theory called a two-parameter foundation model was proposed by Pasternak (1954) for the analysis of the dynamic behavior of beams under moving loads
This paper examines the dynamics responses of a double EulerBernoulli beam system which is elastically connected by a twoparameter Pasternak foundation model under the action of a moving distributed force
Summary
This work is concerned with the study of elastic beams. Beams used in various mechanical systems are subjected to forces which cause them to deform. Fryba (1999), in particular presented a detailed solution techniques to problems of moving loads on Euler-Bernoulli beam supported with one-parameter foundation model. In an attempt to eliminate the shortcoming attributed to one-parameter foundation model, an improved theory called a two-parameter foundation model was proposed by Pasternak (1954) for the analysis of the dynamic behavior of beams under moving loads. This model has been considered to find a physically close and mathematically simple foundation model to represent foundation layer. The method of classical modal expansion was applied to determine the dynamic responses of FUDMA Journal of Sciences (FJS) Vol 4 No 2, June, 2020, pp 1 - 7
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