Vibration mitigation in piezoelectric sandwiched nanocomposite beam-like structures considering Bouc-Wen hysteresis: An adaptive fuzzy sliding mode control approach

Abstract

In this study, an adaptive fuzzy sliding mode controller is proposed to mitigate the vibrations of a hysteretic sandwiched piezoelectric nanocomposite beam regarding system uncertainties, accounting for the intrinsic hysteresis behavior of the actuator layer. The core consists of a graphene sheet-reinforced composite, while the piezoelectric facesheets operate as both sensors and actuators. The actuator's hysteresis is modeled using a Bouc-Wen formulation with uncertain parameters. To compensate for this uncertain nonlinearity and suppress vibrations, an adaptive fuzzy sliding mode controller is developed, with stability guaranteed via Lyapunov's direct method. The results demonstrate the controller's high effectiveness in mitigating mechanical vibrations. The robustness of the proposed controller against parameter uncertainties allows it to manage small variations in structural stiffness and mass resulting from changes in the distribution pattern of the nanocomposite and the piezoelectric thickness ratio. As a result, the controlled deflection of the nanocomposite beam remains unaffected by these two parameters. The most important parameter affecting the controlled response is the type of boundary condition. Decreasing the piezoelectric layer thickness enhances the controller's effort. Due to the hysteresis behavior of the actuator, a steady-state controller effort remains in the system, which is more pronounced for the clamped-clamped nanocomposite beam. The corresponding hysteretic loop shows a similar observation for this boundary condition.