A one-dimensional object is considered that is moving along a flexibly supported plate. It is assumed that the object and the plate are always in contact. The interactive dynamical behavior of the object-plate system is investigated. A self-consistent boundary value problem is formulated, which correctly takes into account the forces of interaction in the moving contact. The critical velocities of the object that distinguish qualitatively different cases of wave-formation are determined. Frequency-energy invariants describing the process of interaction of waves with the object are given. The efficiency of conversion of the wave energy into that of the translation of the object along the plate is studied analytically. The dependence of this efficiency on the velocity velocity of the object and on the frequency of incident wave is analyzed based on the obtained exact solution.
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