This paper is concerned with the problem of controlling the vibration of a distributed system with a support undergoing significant persistent motion. Because of practical considerations, the control is carried out by discrete actuators and sensors. The system is discretized by a new Rayleigh-Ritz approach in which the generalized coordinates represent actual displacements at a given number of points of the system. The control is separated into two parts, one designed to mitigate the effect of the moving support on the absolute motion of the system and the other designed to minimize the remaining absolute motion. A numerical example illustrating the approach is presented.

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