The problem of a two-dimensional elastic system moving on a beam is considered. The moving elastic system or vehicle is represented by the structural members with distributed stiffness, damping, and inertia properties, and it is supported by the suspension units. Each suspension unit consists of a linear spring, a viscous damper, and an unsprung mass. The beam is supported at discrete points along its length, and/or by an elastic foundation. The deformations of the moving system and the beam are represented by their corresponding eigenfunction series. The resulting governing equations are represented by the coupled, ordinary differential equations with variable coefficients. The equations of motion for an elastic platform moving with constant velocity on a beam are derived and solved by the Hamming’s predictor-corrector method. Numerical examples are presented.

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