Dynamic Analysis of Axially Beam on Visco - Elastic Foundation with Elastic Supports under Moving Load

For dynamic analyses of railway track structures, the algorithm of solution is very important. For estimating the important problems in the railway tracks such as the effects of rail joints, rail supports, rail modeling in the nearness of bridge and other problems, the models of the axially beam model on the elastic foundation can be utilized. For studying the effects of axially beam on the elastic foundation, partial differential equations which represent the independent variables should be utilized because of the beams have infinite degrees of freedom. In this paper, solution algorithm and process of the axially beam on the elastic foundation by considering the elastic supports under moving load have been studied and equations have been analyzed as closed form. The beam model includes visco – elastic foundation and elastic supports conditions. For considering the beam element, axial force has been considered beside of shear and moment forces. The solution algorithm is that firstly the differential equations of beam on the elastic foundation with elastic supports are derived and then these equations are solved parametrically by using separation of variables and orthogonality properties of modes. This process and solution have been presented as closed form in this paper. This problem wasn’t investigated in the technical literature. This model can be utilized for the most problems in the railway tracks. The advantage of this paper is presentation of algorithm and process of parametric solution for an axially beam on the visco - elastic foundation with elastic supports.