FORMULATION OF BOUNDARY-VALUE-PROBLEMS FOR THE DYNAMICS OF 2-DIMENSIONAL SYSTEMS WITH MOVING LOADS AND FASTENINGS

A load or fastening is moving in a two-dimensional system without separation. The interdependent dynamical behaviour of these two elements is investigated. The Hamilton variational principle is used to formulate a self-consistent boundary-value problem which correctly incorporates the forces of interaction in the moving contact, including those due to the relative motion and wave pressure. The equations of energy and momentum transport are derived. It is shown that the intermediary through which the vibrational energy of the two-dimensional system is converted into the kinetic energy of the one-dimensional object is the wave pressure force. As an example, a boundary-value problem is formulated for the motion of a beam along a Kirchhoff model plate.