Research in dynamic vibration absorbers has yielded several fundamental designs. Among these are the tuned dynamic absorber, the Lanchester damper, and the impact damper. These designs utilize certain combinations of passive mechanical elements (springs and dampers) to reduce the vibrational amplitude of a system. However, with recent advances in motion sensing and actuating, the design of vibration absorbers that utilize actively actuated elements has become more attractive. This paper develops the theory for using a damped dynamic vibration absorber with an active control element to reduce the vibrational amplitude of a lumped mass system. A control law consisting of a linear combination of velocity and acceleration of the main mass is developed for the active element A closed-form solution is presented for the absorber tuning equation, and numerical methods are used to generate performance curves.

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