Vibrations of a peripherally clamped plate subjected to a concentrated force moving at variable speed

The paper analyzes the vibrations of a rectangular Kirchhoff plate clamped along its perimeter and resting on a Winkler foundation. The elastic plate is characterized by a transversely variable Young’s modulus. The load consists of a concentrated force moving with uniformly variable motion, parallel to the side of the plate. The presented solutions and computational examples describe both forced and free vibrations of the plate.The issue of vibrations of beams and plates on deformable foundations under the influence of moving loads is of particular importance in the analysis of bridge structures as well as road, railway, and airport pavements. One of the most important factors to consider when designing such pavements is the speed of moving vehicles.
In the subject literature, one can find many works devoted to moving loads on beams and plates, including [5-12]. A significant portion of the work is also devoted to the modeling of engineering structures, moving vehicles, and their interaction, for example [1-4], [13]. In the available literature, there is a lack of studies that consider a transversely non-homogeneous plate clamped along its perimeter under a moving load traveling at variable speed.
The paper attempts an analytical solution to this problem. (…)

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