Active Parameter Control of Nonlinear Vibrating Structures

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Abstract
A simple, yet efficient method is presented for the on-line vibration control of nonlinear, multidegree-of-freedom systems responding to arbitrary dynamic environments. The procedure uses nonlinear auxiliary mass dampers with adjustable motion-limiting stops located at selected positions throughout a given nonlinear system. A mathematical model of the system to be controlled is not needed for implementing the control algorithm. The degree of the primary structure oscillation near each vibration damper determines the damper’s actively-controlled gap size and activation time. By using control energy to adjust the damper parameters instead of directly attenuating the motion of the primary system, a significant improvement is achieved in the total amount of energy expended to accomplish a given level of vibration control. In a related paper, the direct method of Lyapunov is used to establish that the response of the controlled nonlinear primary structure is Lagrange stable. Numerical simulation studies of several example systems, as well as an experimental study with a mechanical model, demonstrate the feasibility, reliability, and robustness of the proposed semi-active control method.

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