A methodology is proposed, herein, for reducing the elastodynamic response of high-speed machine systems by introducing a retrofitment scheme which permits these systems to be subjected to an additional dynamical perturbational input which is computer-controlled. This paper is the first of two companion papers which describe a comprehensive analytical and experimental investigation on a breadboard model of the concept, in which the objective is to reduce the vibrational response at the midspan of a flexible rocker link of a four-bar mechanism. A variational formulation is employed to develop the equations of motion governing the response of the flexible member which is subjected to combined parametric and forcing functions. In Part II of these companion papers, the governing equations are solved numerically and the viability of the approach is validated by comparing the analytical predictions with response data from a complementary experimental program.

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