Nonlinear Vibration Control of Smart Porous Sector Plate Reinforced with Agglomerated GPLs

Abstract

The main goal of this research is to analyze the natural frequencies and dynamic response, and to utilize nonlinear control techniques for vibration control of a smart nanocomposite sector plate, while taking into consideration the effects of agglomeration and internal pores. The proposed composite configuration includes a porous core layer reinforced with agglomerated GPLs, as well as two layers of piezoelectric sensors and actuators. Both complete and partial agglomeration states are considered based on the Eshelby–Mori–Tanaka approach to predict the effective properties of the nanocomposite. The mechanical properties of the porous core are characterized using an open-cell metal foam with interconnected pores, notable for their low density and high surface area. The governing equations of motion are derived using Hamilton’s principle, which is based on the First-order Shear Deformation Theory (FSDT) plate theory and the finite element method. The nonlinear fuzzy PID controller is designed as a combination of a fuzzy PI component and a nonlinear PD component. The gains of the PD controller are dynamically adjusted using nonlinear gains to optimize its performance. In addition, a comprehensive analysis has been conducted to examine the effects of geometric dimensions, distribution of reinforcement, weight fractions of nanofillers, parameters of agglomeration, porosity coefficient, porosity pattern, and boundary conditions on the natural frequencies and dynamic response of smart porous nanocomposites. Numerical simulations demonstrate the efficacy of the proposed controller in significantly reducing vibration amplitudes compared to velocity feedback. The velocity feedback controller decreases deflection from 24.39[Formula: see text][Formula: see text] to 8.37[Formula: see text][Formula: see text], whereas the proposed controller achieves 3.66[Formula: see text][Formula: see text]m, representing a 56.27% improvement in performance.