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In this study, a railway superstructure is modeled with a new approach called locally continuous supporting, and its behavior under the effect of moving load is analyzed by using analytical and numerical techniques. The purpose of the study is to demonstrate the success of the new modeling technique.

In the railway superstructure, the support zones are not modeled with discrete spring-damping elements. Instead of this, it is considered to be a continuous viscoelastic structure in the local areas. To model this approach, the governing partial differential equations are derived by Hamilton’s principle and spatially discretized by the Galerkin’s method, and the time integration of the resulting ordinary differential equation system is carried out by the Newmark–Beta method.

Both the proposed model and the solution technique are verified against conventional one-dimensional and three-dimensional finite element models for a specific case, and a very good agreement between the results is observed. The effects of geometric, structural, and loading parameters such as rail-pad length, rail-pad stiffness, rail-pad damping ratio, the gap between rail pads and vehicle speed on the dynamic response of railway superstructure are investigated in detail.

There are mainly two approaches to the modeling of rail pads. The first approach considers them as a single spring-damper connected in parallel located at the centroid of the rail pad. The second one divides the rail pad into several parts, with each of part represented by an equivalent spring-damper system. To obtain realistic results with minimum CPU time for the dynamic response of railway superstructure, the rail pads are modeled as continuous linearly viscoelastic local supports. The mechanical model of viscoelastic material is considered as a spring and damper connected in parallel.

To study the flow of a two‐dimensional, steady, incompressible and constant property fluid over a semi‐infinite flat plate represented by the well‐known Blasius equation.

Differential transform method was used to solve this equation. The solution is based on matching of the inner and outer solutions.

It is observed that the inner solution diverges at η≅5.5 and the outer solution developed for η≥5.5 should be matched with the inner one.

It is the first time, for the best of the authors' knowledge, the missing boundary condition f″(0), related to surface friction, is obtained in a closed form. Also, the matching technique implemented in this study can be used for this type of physical length sensitive problems.

To study the steady magnetohydrodynamic (MHD) flow of a viscous, Newtonian and electrically conducting fluid over a rotating infinite disk with slip boundary condition.

The governing equations, which are partial and coupled, are transformed to ordinary ones by utilizing the similarity variables introduced by Karman and the resulting equation system is solved by using differential transform method.

It is observed that both the slip factor and the magnetic flux decrease the velocity in all directions and thicken the thermal boundary layer.

This paper studies the combined effects of slip and magnetic flux to the flow and thermal fields over a rotating single free disk in an ambient fluid, which were never studied together before.