Adaptive optimal control design for stable vibration attenuation of active constrained layer damping beam structure

Vibration suppression using active constrained layer damping (ACLD) has proven to be an invaluable means for improving the performance of a wide variety of engineering systems. The ACLD creates the hybrid of active and passive damping, attaining favorably high damping characteristics, while at the same time, combines unattractive attributes of both treatments, such as stability sensitivity. Control efforts are needed to achieve an adequate performance of the structures treated with ACLD. The purpose of this research is to investigate theoretically and numerically the adaptive optimal controller of the constrained layer damped beam system, using the classical three-layered distributed-parameter model that utilizes Hamilton\u27s principle in the derivation. Particular emphasis is placed on controlling and stability analysis of the first bending mode of the response on the harmonic excitation using proportional control law. A new technique for prediction of optimal damping performance for fully treated beam/ACLD system using time-domain analysis of control is proposed. Comparison between analytical and numerical results, as well with experimental results found in the literature, showed that the proposed strategy is very simple and efficient in constructing the adaptive optimal control gains for amplitude attenuation of structural vibrations